8414 lines
348 KiB
Plaintext
8414 lines
348 KiB
Plaintext
Precision Measurement and Fundamental Constants II
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Proceedings of the Second International Conference held at the National Bureau of Standards Gaithersburg, MD, June 8-12, 1981 Edited by:
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B.N. Taylor and W.D. Phillips
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Center for Basic Standards National Measurement Laboratory National Bureau of Standards
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Gaithersburg, MD 20899
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U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary
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NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director Issued August 1 984
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Library of Congress Catalog Card Number: 84-601083 National Bureau of Standards Special Publication 617 Natl. Bur. Stand. (U.S.), Spec. Publ. 617, 646 pages (Aug. 1984)
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CODEN: XNBSAV
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U.S. GOVERNMENT PRINTING OFFICE
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WASHINGTON: 1984 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
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Abstract
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This volume presents the Proceedings of the Second International Conference on Precision Measurement and Fundamental Constants, held at the National Bureau of Standards in Gaithersburg,
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MD, from June 8-12, 1981. Like its 1970 predecessor, the Conference provided an international
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forum for theoretical, experimental, and applied scientists actively engaged in research on precision measurements relating to the fundamental physical constants, and on the testing of related fundamental theory. More specifically, the purpose of the Conference was to assess the present state of the precision measurement-fundamental constants field, to examine basic limitations, and to explore the prospects for future significant advances. The principal subjects covered were: frequency, wavelength, spectroscopy, quantum electrodynamics, the gas constant, x-ray interferometry, nuclidic masses, uncertainty assignment, gravitational acceleration, mass, electrical quantities, gravity, and relativity. These proceedings contain the vast majority of both the invited review papers and the contributed current research papers presented at the Conference. The new results reported at the Conference were considered for inclusion in the 1983 least-squares adjustment of the constants carried out under the auspices of the Task Group on Fundamental Constants of the
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Committee on Data for Science and Technology (CODATA). Key words: data analysis; experimental tests of theory; fundamental constants; least-squares ad-
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justments; precision measurements.
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iii
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Preface
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Like its 1970 predecessor, the Second International Conference on Precision Measurement and Fundamental Constants (PMFC-II), held at the National Bureau of Standards, Gaithersburg, MD, June 8-12, 1981, provided an international forum for scientists actively engaged in experimental and theoretical research on precision measurements relating to the fundamental physical constants, and on the testing of related fundamental theory. More specifically, the Conference assessed the present state of the precision measurement-fundamental constants (PMFC) field, examined its current limitations, and explored the prospects for future significant advances.
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The Conference was unique in that it brought together to an even greater extent than did PMFC-
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I scientists from fields as apparently diverse as precision mass metrology and quantum field theory. But this of course was the main reason for holding the Conference; that is, its principal purpose was to foster the interchange of information and ideas among researchers who at first glance have Httle in common but who upon closer scrutiny have much to gain from each other because of their mutual interest in and need for precision measurements and accurate values of the fundamental constants. The reasons for this interest and need were well described in the Preface to the proceedings of PMFC-I by D. N. Langenberg and B. N. Taylor:
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Precision measurement plays an essential and crucial role in the development of all science and technology. Scientific theories cannot be tested, instruments and machines cannot be designed and built, and even the daily routine of the market place cannot proceed without precise quantitative measurement. The demand for precision and accuracy is greatest at the frontiers of science and technology. Here our increasing understanding of the fundamental nature of the universe and our increasing ability to put our knowledge to practical use depends on continuing refinement of our theories and of the technology used in testing these theories against reality.
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In all of our fundamental theories there appear a certain few parameters which characterize the fun-
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damental particles and interactions we find in nature. These are the fundamental physical constants. The precision determination of the numerical values of these constants has long been and remains one
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of the principal objectives of experimental science. This is not because there is any intrinsic virtue in accumulating lists of ever longer numbers, but because the fundamental constants are the quantitative
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links between our most basic theories and the physical reality we wish them to describe. Our theories must stand or fall according to their ability to make quantitative predictions which agi-ee with experimental observations to the maximum accuracy possible. The progress of our understanding of the physical world is therefore very much intertwined with the advance of the art of precision measurement and
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its application to the determination of the fundamental physical constants.
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To this we must add the idea that because of the interrelationships which exist among the fun-
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damental constants and related quantities, for example, the proton gyromagnetic ratio, the Fara-
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day, Avogadro, and fine-structure constants, 2e//? via the Josephson effect, the absolute ohm and ampere, the quantized Hall resistance, the electron and muon anomalous magnetic moments, the
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proton to electron mass ratio, etc., it is appropriate, indeed even necessary, for the solid state theorist to be aware of the work of the electrical metrologist; the atomic mass spectroscopist of the work of the precision electrochemist; and the quantum electrodynamics theorist of the work of the experimental semiconductor physicist. The fundamental constants of nature and closely related
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precision measurements are truly the common meeting ground for many of the disciplines of sci-
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ence and technology.
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The technical program of the Conference was designed to give participants both a broad and in-
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depth view of the PMFC field as well as many opportunities to interact with one another. The
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Keynote Address by Ian W. Roxburgh served to stimulate thinking about the fundamental con-
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stants and their relationship to the laws of nature; the invited review talks provided a broad over-
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PMFC view of the
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field including its current limitations and future possibilities; the orally
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presented contributed papers gave a more detailed sampling of the current research underway in
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the field; the five poster sessions (one each day with about 20 papers per session) allowed every-
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one to hold in-depth discussions of their current research work with interested colleagues; and the
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informal, off the record, evening session enabled those who were sufficiently brave to present
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their most highly speculative or "far out" ideas.
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— — Each day of the Conference was devoted to a small number of broad topical areas and each of
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the papers presented that day invited review, oral contributed, and poster more or less dealt with the selected topics. This arrangement has been followed in this volume except for slight modifications in order to improve overall coherence. Thus, included in these Proceedings are the written versions of the Keynote Address, the 21 invited review papers (one in abstract form only), the 16 oral contributed papers (one in abstract form only); and 93 of the 100 poster papers (one in abstract form only). Nothing has been included from the evening session because it was truly "off
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the record."
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V
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A quick perusal of the contents of these Proceedings would convince even the most casual observer
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that the precision measurement-fundamental constants field is full of vitality. Enormous advances have been made over the last decade or so since PMFC-I. The uncertainty in c, the speed of light, is now limited by the present *^^Kr definition of the meter; a definition of length based on c is destined to replace the krypton definition within the next several years. The Rydberg constant is now known to one part in 10^, the Avogadro constant to one part in 10^, the fine structure constant to one part in 10"^, the Faraday constant to better than two parts in 10^, the proton-to-electron mass ratio and proton gyromagnetic ratio to two parts in 10'^, the anomalous moment of the electron to 3 parts in 10^, and the Newtonian gravitational constant to 6 parts in 10^. On the theoretical side, significant advances have been made in the theory of the anomalous moment of the electron and muon, Lamb-shift, and muonium hyperfine splitting. Moreover, completely new techniques and
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phenomena which promise to have a significant impact on the future of the PMFC field have been
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developed and identified. Especially noteworthy in this regard is the methodology for trapping a single, charged particle pioneered by H. G. Dehmelt and colleagues, and the discovery of the
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quantized Hall resistance by K. v. Klitzing. This latter phenomenon, which may eventually yield
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the most accurate value of the fine-structure constant, has already attracted considerable attention
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since it was first reported in June 1980 as evidenced by the eight papers on the subject presented
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PMFC at the Conference. It could have the same impact on the
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field in the 1980's as did the
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Josephson effect in the 1960's.
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The one to two orders of magnitude reduction in the uncertainties of many of the constants which has taken place since PMFC-I continues the trend of the last 20 to 30 years and again raises the
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question as to whether it can continue indefinitely. Will improvements in and the appHcation of
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existing technologies such as high-speed computers, lasers, and cryogenics, and the discovery of
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new techniques and phenomena, allow the proceedings editors of a hypothetical PMFC-III to make
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the same comment a decade or so hence? We are incHned to beUeve that those editors will be able
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to do so, especially if the enthusiasm of the Conference participants was any indication of what hes ahead. In this regard we were especially pleased to see so many in attendance from outside of the United States (103 out of 257 or 40%) and to see the large number of graduate students who are being trained to become the next generation of "precision measurers."
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We would like to thank personally the many organizations and individuals who helped to make
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PMFC-II the highly worthwhile Conference it turned out to be. These include its sponsors, contributors, and the members of the organizing committees as listed on the following pages, as well as many members of the staff of the National Bureau of Standards, especially Joanne Lorden,
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Greta Pignone, and Kathy Stang.
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B. N. Taylor
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W. D. Phillips
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vi
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Conference Organizing Committees
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Conference Committee
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K. M. Baird (National Research Council, Canada) E. R. Cohen (Science Center, Rockwell International, U.S.A.) R. D. Deslattes (National Bureau of Standards, U.S.A.) J. L. Hall (Joint Institute for Laboratory Astrophysics, U.S.A.) K. G. Kessler (National Bureau of Standards, U.S.A.) D. Kleppner (Massachusetts Institute of Technology, U.S.A.) D. R. Lide (National Bureau of Standards, U.S.A.) R. C. Ritter (University of Virginia, U.S.A.)
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W. G. Schweitzer (National Bureau of Standards, U.S.A.) B. N. Taylor (Chairman; National Bureau of Standards, U.S.A.)
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International Advisory Committee
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S. J. Brodsky (Stanford Linear Accelerator Center, U.S.A.) H. G. Dehmelt (University of Washington, U.S.A.) V. I. Goldansky (Institute for Chemical Physics, U.S.S.R.) T. W. Hansch (Stanford University, U.S.A.) H. W. Hellwig (Frequency and Time Systems, Inc., U.S.A.) T. Kinoshita (Cornell University, U.S.A.) B. Kramer (Physikahsch-Technische Bundesanstalt, F.R.G.) M. Morimura (National Research Laboratory of Metrology, Japan) B. W. Petley (National Physical Laboratory, U.K.) T. G. Quinn (Bureau International des Poids et Mesures, France) N. F. Ramsey (Harvard University, U.S.A.) A. Rich (University of Michigan, U.S.A.)
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Honorary Committee
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E. Ambler (National Bureau of Standards, U.S.A.) W. R. Blevin (CSIRO Division of Applied Physics, Australia) L. M. Branscomb (International Business Machines Corporation,
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U.S.A.)
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P. Dean (National Physical Laboratory, U.K.)
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A. Ferro-Milone (Institute Elettrotechnico Nazionale "Galileo Ferraris," Italy)
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P. Giacomo (Bureau International des Poids et Mesures, France) Kanjie Ju (National Institute of Metrology, P.R.C.) M. Kawata (National Institute of Metrology, Japan) D. Kind (Physikahsch-Technische Bundesanstalt, F.R.G.) H. Preston-Thomas (National Research Council, Canada) Y. V. Tarbeyev (Mendelelyev Research Institute of Metrology,
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U.S.S.R.) J. Terrien (Bureau International des Poids et Mesures, France)
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vii
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—
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Sponsors
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International Union of Pure and Applied Physics
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Committee on Data for Science and Technology of the International Council of Scientific Unions
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U.S. National Academy of Sciences National Research Council, Committee on Fundamental Constants
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Bureau International des Poids et Mesures
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National Bureau of Standards U.S. Department of Commerce
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Contributors
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The Second International Conference on Precision Measurement and Fundamental Constants expresses its deep appreciation to the following organizations for their generous financial support which contributed greatly to making this meeting possible.
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Airco, Inc.
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Avco Corporation Ball Technical Products Group Beckman Instruments, Inc.
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Bendix Automation & Measurement Division
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COMSAT Laboratories
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Corning Glass Works E.I. duPont de Nemours & Company, Inc.
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EG&G Princeton Applied Research Corporation
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Electro Scientific Industries, Inc.
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Exxon Research and Engineering Company Fisher Scientific Company John Fluke Mfg. Co., Inc. The Foxboro Company Frequency and Time Systems, Inc. General Atomic Company General Electric Company
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Guildline Instruments Inc.
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Gulf Research & Development Company
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Hewlett-Packard Company
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IEEE Instrumentation and Measurement Society
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International Business Machines Corporation
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International Union of Pure and Applied Physics
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Leeds & Northrup Company
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Matheson Gas Products Mettler Instrument Corporation
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The 3M Company
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Mobil Research and Development Corporation Monsanto Company Motorola Inc. National Bureau of Standards National Conference of Standards Laboratories National Science Foundation Rockwell International
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Sandia Laboratories
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Shell Development Company
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Tektronix, Inc. Texas Instruments, Inc. U.S. Air Force Geophysics Laboratory
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U.S. Army Research Office
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U.S. Office of Naval Research Westinghouse Electric Corporation Xerox Corporation
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viii
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ix
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Contents
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Preface Conference Organizing Committees Conference Sponsors and Contributors Frontispiece
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Keynote Address: The Laws and Constants of Nature I. W. Roxburgh
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Page v
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vii viii
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ix
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1
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Frequency, Wavelength, and Stored Ions
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Frequency Standards Based on Magnetic Hyperfine Structure Resonances (Review)
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11
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H. Hellwig
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Performance of the Three NRC 1-Meter CsVI Primary Clocks
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21
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A. G. Mungall, H. Daams, and J.-S. Boulanger
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Prospects for Cesium Primary Standards at the National Bureau of Standards
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25
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L. L. Lewis, F. L. Walls, and D. A. Howe
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A Cesium Beam Atomic Clock with Laser Optical Pumping, as a Potential
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Frequency Standard
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29
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M. Arditi
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Frequency Measurement of Optical Radiation (Review)
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35
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K. M. Baird
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Optical Frequency Standards: Progress and Applications (Review; abstract only)
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43
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J. L. Hall
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Measurement of Frequency Differences of Up to 170 GHz Between Visible
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Laser Lines Using Metal- Insulator-Metal Point Contact Diodes
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45
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H.-U. Daniel, M. Steiner, and H. Walther
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Precision Frequency Metrology for Lasers in the Visible and Apphcation to Atomic
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Hydrogen ,
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49
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B. Burghardt, H. Hoeffgen, G. Meisel, W. Reinert, and B. Vowinkel
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System for Light Velocity Measurement at NRLM
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53
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K. Tanaka, T. Sakurai, N. Ito, T. Kurosawa, A. Morinaga, and S. Iwasaki
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'Laser Wavelength Measurements and Standards for the Determination of Length (Review) ... 57 W. R. C. Rowley
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Double-Mode Method of Sub-Doppler Spectroscopy and Its Apphcation in Laser
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Frequency Stabilization
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65
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N. G. Basov, M. A. Gubin, V. V. Nikitin, A. V. Nikulchin,
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D. A. Tyruikov, V. N. Petrovskiy, and E. D. Protscenko
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He-Ne C'-n.,) Lasers at 0.633 ixm (and at 0.604 (xm)
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69
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F. Bertinetto, B. I. RebagHa, P. Cordiale, S. Fontana, and G. B. Picotto
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Recent Work on 612 nm He-Ne Stabilized Lasers
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73
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A. Brillet, P. Cerez, and C. N. Man-Pichot
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Iodine and Methane Stabilized He-Ne Lasers as Wavelength Standards
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77
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Wu Shen Nai-cheng,
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Yao-xiang, Sun Yi-min, Li Cheng-yang,
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Zhang Xue-bin, and Wang Chu
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xi
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Spatial Coherence and Optical Wavelength Metrology P. Bouchareine
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Spectroscopy of Stored Ions (Review) D. J. Wineland
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Progress Toward a Stored Ion Frequency Standard at the National Bureau of Standards W. M. Itano, D. J. Wineland, J. C. Bergquist, and F. L. Walls
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High Resolution Microwave Spectroscopy on Trapped Ba^ Ions W. Becker, R. Blatt, and G. Werth
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Observation of High Order Side Bands in the Spectrum of Stored ^He^ Ions H. A. Schuessler and H. S. Lakkaraju
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Quantum Limits in the Measurements of e.m. Fields and Frequency (Abstract only)
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V. B. Braginsky
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Spectroscopy, Quantum Electrodynamics, and Elementary Particles
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Precision Laser Spectroscopy (Review)
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T. W. Hansch
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Atomic Beam, Linear, Single-Photon Measurement of the Rydberg Constant S. R. Amin, C. D. Caldwell, and W. Lichten
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Current Work on Two Photon Excitation in a Hydrogen Beam for the
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Measurement of the Rydberg Constant and mjmp
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D. Shiner and C. Wieman
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Measurement of the 2^P3/2- 2'^Sy2 Fine-Structure Interval in Atomic Hydrogen K. A. Safinya, K. K. Chan, S. R. Lundeen, and F. M. Pipkin
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Measurement of the Lamb Shift in Hydrogen, n = 2
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S. R. Lundeen and F. M. Pipkin
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Atomic Interferometer Method Measurement of the Lamb Shift in Hydrogen (n = 2)
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Y. L. Sokolov
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Measurement of the 4'^Sy2 - 4'^'Pv2 Lamb Shift in He+
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J. J. Bollinger, S. R. Lundeen, and F. M. Pipkin
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Lamb Shift in the Hydrogenic Ion CU"^ E. T. Nelson, 0. R. Wood II, C. K. N. Patel, M. Leventhal, D. E. Murnick, H. W. Kugel, and Y. Niv
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Helium Fine Structure and the Fine Structure Constant W. Frieze, E. A. Hinds, A. Kponou, V. W. Hughes, and F. M. J. Pichanick
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Preliminary Measurement of the J = 0 to / = 2 Fine Structure Interval in the 3 ^P State of Helium M. Feldman, T. Breeden, L. DiMauro, T. Dong, and H. Metcalf
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Laser Microwave Precision Measurements of 2 -^Si and 2 '^P Term Splittings
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in Helium-Like Li^ U. Kotz, J. Kowalski, R. Neumann, S. Noehte, H. Suhr, K. Winkler, and G. zu Putlitz
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An Optically Pumped Metastable Hydrogen Beam
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K. C. Harvey
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Precise Determination of the S and P Quantum Defects in Sodium and Cesium by Millimeter and Submillimeter Spectroscopy Between Rydberg States P. Goy, J. M. Raimond, G. Vitrant, C. Fabre, S. Haroche, and M. Gross
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A New Method of Measuring the Fine-Structure Constant Using Stark Spectroscopy
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M. G. Liftman and W. D. Phillips
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Time Resolved Sub-Natural Width Spectroscopy W. D. Phillips and H. J. Metcalf
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xii
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Page
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81 83 93 99 103 109
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Ill 117
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123 127 131 135 141 145
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149 153
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159 163 169 173 177
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The Spectroscopy of Atoms and Molecules in Gases: Corrections to the
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Doppler-Recoil Shift
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M. P. Haugan and F. V. Kowalski
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The Implications of QED Theory for the Fundamental Constants (Review)
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G. P. Lepage and D. R. Yennie
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QED Uncertainties in
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Fine Structure Calculations
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G. W. Erickson
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Sixth Order Contributions to g-2 of the Electron M. J. Levine and R. Z. Roskies
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Calculation of the Eighth Order Anomalous Magnetic Moment of the Electron T. Kinoshita and W. B. Lindquist
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Experimental Determinations of the Anomalous Magnetic Moments of the Free
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Leptons (Review)
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R. Conti, D. Newman, A. Rich, and E. Sweetman
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Preliminary Comparison of the Positron and Electron Spin Anomalies P. B. Schwinberg, R. S. Van Dyck, Jr., and H. G. Dehmelt
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— Geonium Without a Magnetic Bottle A New Generation
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G. Gabrielse and H. Dehmelt
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The Magnetic Moment of Positive Muons in Units of the Proton Magnetic Moment E. Klempt, R. Schulze, H. Wolf, M. Camani, F. N. Gygax, W. Riiegg,
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A. Schenck, and H. Schilling
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Measured Gy-Factor Ratio of "He^d ^Sy2) and ^He(2 ^Si)
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H. G. Robinson and C. E. Johnson
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Determination of the Neutron Magnetic Moment G. L. Greene, N. F. Ramsey, W. Mampe, J. M. Pendlebury, K. Smith, W. B. Dress, P. D. Miller, and P. Perrin
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Precision Exotic Atom Spectroscopy (Review) V. W. Hughes
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Fundamental Tests and Measures of the Structure of Matter at Short Distances (Review) S. J. Brodsky
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Experimental Limit for the Charge of the Free Neutron
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R. Gahler, J. Kalus, and W. Mampe
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Gas Constant, X-Ray Interferometry, Nuclidic Masses, Other Constants, and Uncertainty Assignment
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Methods for the Determination of the Gas Constant (Review) A. R. Colclough
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An Ultrasonic Determination of the Gas Constant W. C. Sauder
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Spherical Acoustic Resonators: Promising Tools for Thermometry and Measurement of the Gas Constant M. R. Moldover and J. B. Mehl
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Proposed Method for the Determination of the Molar Gas Constant, R
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L. A. Guildner and M. L. Reilly
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A Radiometric Determination of the Stefan-Boltzmann Constant
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T. J. Quinn and J. E. Martin
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NRLM On the Radiometric Measurement of the Stefan-Boltzmann Constant at
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A. Ono
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Applications of X-ray Interferometry (Review) R. D. Deslattes
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Work Related to the Determination of the Avogadro Constant in the PTB
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P. Seyfried
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xiii
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Page
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181 185 195 201 203 207 215 219 223 229 233
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237 249 257
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263 277
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281 287 291 299 303 313
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Page
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Absolute Determination of the (220)-Lattice Spacing in Silicon
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317
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P. Becker and H. Siegert
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Systematic Uncertainties in the Determination of the Lattice Spacing d(220) in Silicon
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321
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H. Siegert and P. Becker
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High Precision Studies of Pionic X Rays: Some Past Results and Future Prospects
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325
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G. Dugan, L. Delker, C. S. Wu, and D. C. Lu
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Isotope Shifts of K X-Rays of Lead
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331
|
|
|
|
G. L. Borchert, 0. W. B. Schult, J. Speth, P. G. Hansen, B. Jonson,
|
|
|
|
H. Ravn, and J. B. McGrory
|
|
|
|
The Measurement of Atomic Masses by Mass Spectroscopic Methods and a
|
|
|
|
Role for Atomic Masses in the Determination of the Fundamental
|
|
|
|
Constants (Review)
|
|
|
|
335
|
|
|
|
W. H. Johnson
|
|
|
|
Absolute Determination of the Threshold Energies of "Li(p,n), ^"B(p,n), and '^N(p,n)
|
|
|
|
345
|
|
|
|
P. H. Barker, M. J. Lovelock, H. Naylor, R. M. Smythe, and R. E. White
|
|
|
|
Preliminary Proton/Electron Mass Ratio Using a Precision Mass-Ratio Spectrometer
|
|
|
|
349
|
|
|
|
R. S. Van Dyck, Jr. and P. B. Schwinberg
|
|
|
|
A Direct Determination of the Proton-Electron Mass Ratio
|
|
|
|
353
|
|
|
|
G. Graff, H. Kalinowsky, and J. Traut
|
|
|
|
A New Determination of the Atomic Weight of Silver and an Improved Value
|
|
|
|
for the Faraday
|
|
|
|
357
|
|
|
|
L. J. Powelh T. J. Murphy, and J. W. Gramhch
|
|
|
|
High Resolution Magnetic Measurements on Rotating Superconductors to Determine hhyi^
|
|
|
|
359
|
|
|
|
B. Cabrera, S. B. Felch, and J. T. Anderson
|
|
|
|
High Precision Measurement of the Electron Compton Wavelength ihlm^.) Using
|
|
|
|
Cryogenic Metrological Techniques
|
|
|
|
365
|
|
|
|
j. C. Gallop, B. W. Petley, and W. J. Radcliffe
|
|
|
|
Preliminary Determination of
|
|
|
|
369
|
|
|
|
E. Kriiger, W. Nistler, and W. Weirauch
|
|
|
|
The Assignment of Uncertainties to the Results of Experimental Measurements (Review)
|
|
|
|
375
|
|
|
|
J. W. Muller
|
|
|
|
On the Statement of a Total Confidence Interval Based on the Concept of
|
|
Randomization of Systematic Errors: Large and Small Sample Sizes W. Woger
|
|
|
|
^ 383
|
|
|
|
Measurement Assurance
|
|
|
|
385
|
|
|
|
A. F. Dunn
|
|
|
|
An Extended-Least -Squares Treatment of Discrepant Data
|
|
|
|
391
|
|
|
|
E. R. Cohen
|
|
|
|
Gravitational Acceleration, Mass, and Electrical Quantities
|
|
|
|
Present Status of the Absolute Measurement of Gravitational Acceleration (Review)
|
|
|
|
397
|
|
|
|
A. Sakuma
|
|
|
|
A New, Portable, Absolute Gravimeter
|
|
|
|
405
|
|
|
|
M. A. Zumberge, J. E. Faller, and R. L. Rinker
|
|
|
|
— "Super Spring" A Long Period Vibration Isolator
|
|
|
|
411
|
|
|
|
R. L. Rinker and J. E. Faller
|
|
|
|
Transportable Gravimeter for the Absolute Determination of Gravity
|
|
|
|
419
|
|
|
|
Guo You-guang, Huang Da-lun, Li De-xi, Zhang Guang-yuan, Gao Jing-long,
|
|
|
|
Fang Yong-yuan, and Huang Cheng-qing
|
|
|
|
New Techniques for Absolute Gravity Measurement
|
|
|
|
423
|
|
|
|
J.A.Hammond, R. L. liiff, and R. W. Sands
|
|
|
|
xiv
|
|
|
|
The Mass Unit "Kilogram," Precision Measurement of Mass, Attainable
|
|
Uncertainties, and Possibilities of a New Definition (Review)
|
|
|
|
M. Kochsiek
|
|
|
|
.
|
|
|
|
Page 427
|
|
|
|
Measurement of Air Density for High Accuracy Mass Determination
|
|
|
|
437
|
|
|
|
D. B. Prowse
|
|
|
|
On a More Precise Correction for Buoyancy and Gas Adsorption in Mass Measurement
|
|
|
|
441
|
|
|
|
Y. Kobayashi
|
|
|
|
— Density Standards The Density and Thermal Dilatation of Water
|
|
|
|
445
|
|
|
|
G. A. Bell and J. B. Patterson
|
|
|
|
— Precision Measurements on Solid Artifacts for a Redetermination of the Density of Water
|
|
|
|
449
|
|
|
|
A. Peuto, A. Sacconi, R. Panciera, W. Pasin, and M. Rasetti
|
|
|
|
The Influence of Dissolved Air on the Density of Water
|
|
|
|
453
|
|
|
|
G. Girard and M.-J. Coarasa
|
|
|
|
The Helium Melting Curve and the Linkage of Fundamental Constants,
|
|
|
|
Pressure, Density, and Mass
|
|
|
|
,
|
|
|
|
457
|
|
|
|
C. T. Van Degi'ift
|
|
|
|
Reahzation of the Electrical SI Units (Review)
|
|
|
|
461
|
|
|
|
B. P. Kibble
|
|
|
|
An Absolute Determination of the Volt at LCIE
|
|
|
|
465
|
|
|
|
N. Elnekave and A. Fau
|
|
|
|
The CSIRO Absolute Volt Project
|
|
|
|
469
|
|
|
|
G. J. Sloggett, W. K. Clothier, D. J. Benjamin, M. F. Currey, and H. Bairnsfather
|
|
|
|
Status of the Measurement of the NBS Ampere in SI Units
|
|
|
|
475
|
|
|
|
P. T. Olsen, W. D. Phillips, and E. R. Williams
|
|
|
|
A Feasibihty Study of an Absolute Determination of the Magnetic Flux Quantum
|
|
|
|
479
|
|
|
|
K. Hara, F. Shiota, and T. Kubota
|
|
|
|
The Work Done at the Mendeleyev Research Institute of Metrology (VNIIM)
|
|
|
|
To Improve the Values of the Fundamental Constants
|
|
|
|
483
|
|
|
|
Y. V. Tarbeyev
|
|
|
|
Reahzation of a Josephson Potentiometer
|
|
|
|
489
|
|
|
|
M. Koyanagi, T. Endo, and A. Nakamura
|
|
|
|
A Transportable Josephson Voltage Standard
|
|
|
|
493
|
|
|
|
K. Lahdenpera, H. Seppa, and P. Wallin
|
|
|
|
— The Proton Gyromagnetic Ratio in HoO A Problem in Dimensional Metrology (Review)
|
|
|
|
497
|
|
|
|
E. R. Williams, P. T. Olsen, and W. D. Phillips
|
|
|
|
The Development of Precision Measurement and Fundamental Constants in China
|
|
|
|
505
|
|
|
|
Wang Zhu-xi
|
|
|
|
The 7p-Experiment at PTB
|
|
|
|
509
|
|
|
|
K. Weyand
|
|
|
|
A New Method for the Determination of the Proton Gyromagnetic Ratio
|
|
|
|
515
|
|
|
|
G. L. Greene
|
|
|
|
The Quantized Hall Resistance in Two-Dimensional Systems (Review)
|
|
|
|
519
|
|
|
|
K. von Klitzing, H. Obloh, G. Ebert, J. Knecht, and K. Ploog
|
|
|
|
MOS Hall Effect in Silicon
|
|
|
|
Inversion Layers for hle^ Determination
|
|
|
|
529
|
|
|
|
C. Yamanouchi, K. Yoshihiro, J. Kinoshita, K. Inagaki, J. Moriyama,
|
|
|
|
S. Baba, S. Kawaji, K. Murakami, T. Igarashi, T. Endo, M. Koyanagi,
|
|
|
|
and A. Nakamura
|
|
|
|
Cryogenic Method for the Determination of the Fine-Structure Constant
|
|
|
|
by the Quantized Hall Resistance
|
|
|
|
535
|
|
|
|
E. Braun, P. Gutmann, G. Hein, F. Melchert, P. Warnecke, S. Q. Zue, and K. v. Klitzing
|
|
|
|
XV
|
|
|
|
Status of the NBS-NRL Determination of the Fine-Structure Constant
|
|
Using the Quantized Hall Resistance Effect
|
|
M. E. Cage, R. F. Dziuba, B. F. Field, C. F. Lavine, and R..J. Wagner
|
|
Use of a Cryogenic Current Comparator to Determine the Quantized Hall
|
|
Resistance in a Silicon MOSFET
|
|
A. Hartland
|
|
A Resistance Standard Using the Quantized Hall Resistance of
|
|
GaAs-Al,Gai„ ,.As Heterostructures A. C. Gossard and D. C. Tsui
|
|
A Quantitative Theory for the Determination oihie- from the Hall Effect in
|
|
Two-Dimensional Conductors L. BHek and G. Hein
|
|
Quantum Hall Effect: Role of Inversion Layer Geometry and Random Impurity Potential R. W. Rendell and S. M. Girvin
|
|
|
|
Page
|
|
539 543 549 553 557
|
|
|
|
Gravity and Relativity
|
|
|
|
Experiments Relating to the Newtonian Gravitational Constant (Review)
|
|
|
|
561
|
|
|
|
H. de Boer
|
|
|
|
Redetermination of the Newtonian Gravitational Constant "G"
|
|
|
|
573
|
|
|
|
G. G. Luther and W. R. Towler
|
|
|
|
The Design of a Beam Balance for a Determination of G
|
|
|
|
577
|
|
|
|
C. C. Speake and A. J. F. Metherell
|
|
|
|
Optimizing the Shape of the Attracting Mass in Precision Measurements of G
|
|
|
|
581
|
|
|
|
A. J. F. Metherell, C. C. Speake, Y. T. Chen, and J. E. Faller
|
|
|
|
Vacuum Polarization and Recent Measurements of the Gravitational
|
|
|
|
Constant as a Function of Mass Separation
|
|
|
|
587
|
|
|
|
D. R. Long
|
|
|
|
Tests of the Gravitational Inverse Square Law Using Torsion Balances
|
|
|
|
591
|
|
|
|
J. K. Hoskins, R. Newman, J. Schultz, and R. Spero
|
|
|
|
Measurement of Gravitational Forces at Separations Around 10 Meters
|
|
|
|
595
|
|
|
|
H. Yu, W. Ni, C. Hu, F. Liu, C. Yang, and W. Liu
|
|
|
|
Non-Newtonian Gravity: Geophysical Evidence
|
|
|
|
597
|
|
|
|
F. D. Stacey and G. J. Tuck
|
|
|
|
Experimental Test of a Spatial Variation of the Newtonian Gravitational
|
|
|
|
Constant at Large Distances
|
|
|
|
601
|
|
|
|
H. A. Chan and H. J. Paik
|
|
|
|
The Measurement of G for Small Inter-Mass Spacings
|
|
|
|
607
|
|
|
|
W. C. Oelfke
|
|
|
|
Tests of Gravitation and Relativity (Review)
|
|
|
|
611
|
|
|
|
R. F. C. Vessot
|
|
|
|
Is the Gravitational Constant Changing?
|
|
|
|
625
|
|
|
|
T. C. Van Flandern
|
|
|
|
Experiments on Variation of the Gravitational Constant Using Precision Rotations
|
|
|
|
629
|
|
|
|
G. T. Gillies and R. C. Ritter
|
|
|
|
Interpreting Dirac's Large Numbers Hypothesis
|
|
|
|
635
|
|
|
|
W. Davidson
|
|
|
|
New Laboratory Test of the Equivalence Principle
|
|
|
|
639
|
|
|
|
P. T. Keyser, J. E. Faller, and K. H. McLagan
|
|
|
|
What Test Masses Are Best for an Eotvos Experiment?
|
|
|
|
643
|
|
|
|
D. F. Bartlett, J. Shepard, and C. D. Zafiratos
|
|
|
|
xvi
|
|
|
|
Equivalence Principles and Precision Measurements W. Ni
|
|
An Inertial Clock to Test the Non-Metricity of Gravity W. S. Cheung and R. C. Ritter
|
|
Assessment of the Prospects for a Measurement of Relativistic Frame Dragging by 1990 R. A. Van Patten
|
|
The Status of the Velocity of Light in Special Relativity E. Breitenberger
|
|
Relativistic Time Dilation: A Latter-Day Ives-Stillwell Experiment
|
|
P. Nachman, M. D. Rayman, and J. L. Hall
|
|
An Experiment to Measure Relative Variations in the One-Way Velocity of Light
|
|
D. G. Torr and P. Kolen
|
|
High-Energy Gamma Rays Might Be Faster than Visible Light
|
|
K. Fujiwara
|
|
Fiber Optic Ring as a Gravitational Wave Detector
|
|
C. L. Mehta, D. Ranganathan, and G. Bose
|
|
A Possible Laser Gravitational Wave Experiment in Space (Abstract only)
|
|
J. E. Faller and P. L. Bender
|
|
Author Index
|
|
Conference Registrants
|
|
|
|
Page 647
|
|
653 659 667 671 675 681 685 689 691 695
|
|
|
|
Papers in this volume, except those by National Bureau of Standards authors, have not been significantly altered by the National Bureau of Standards. Opinions expressed in non-NBS papers
|
|
are those of the authors, and not necessarily those of the National Bureau of Standards. Non-NBS
|
|
authors are solely responsible for the content and quality of their submissions. The mention of trade names in the volume is in no sense an endorsement or recommendation by
|
|
the National Bureau of Standards.
|
|
xvii
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
KEYNOTE ADDRESS
|
|
The Laws and Constants of Nature
|
|
Ian W. Roxburgh
|
|
Department of Applied Mathematics, Queen Mary College, University of London
|
|
The paper concentrates on a few problems; geometry, mechanics, gravitation, and the large
|
|
numbers {10'^^) that relate microphysics to the large scale stracture of the universe. My purpose is not
|
|
so much to describe what is known, but to question how well anything is known and to provoke the
|
|
reader into asking questions and proposing experiments that probe the foundations of our understand-
|
|
ing. Is geometry locally Euclidean? Do different clocks keep the same time? Does our existence depend on the exact form of the laws of nature and the exact values of the constants of nature? Do the con-
|
|
stants of nature vary in time? Why are there laws at all? Readers can, and I hope will, add questions of
|
|
their own.
|
|
Key words: anthropic principle; constants of nature; fundamental natural laws; gra\itation; large number hypothesis; time variation of constants.
|
|
|
|
1. Introduction
|
|
Science as we know it probably began with man's at-
|
|
tempts to understand the regularity of nature as seen in the rising and setting of the sun, the phases of the moon, the annual recurrence of the seasons, and the motion of the planets across the sky. Indeed, the Shu Ching, the ancient Chinese Book of History, opens in the Cannon of Yao with the sovereign giving instructions [1]:
|
|
"He commanded the brothers Hsi and the brothers
|
|
Ho, in reverent accord with their observations of the wide heavens, to calculate and delineate the movements of the sun, the moon, the stars and the zodiacal spaces and so to deliver respectfully the seasons to be observed by the people."
|
|
Science in those days was a dangerous activity; we later learn that the astronomers Hsi and Ho were executed for
|
|
failing to predict a solar ecUpse. If the supporting details
|
|
are correct (the moon was in Sieou Fang in the center of Tsing Lung on the first day of autumn) this was in the
|
|
year 2137 B.C.
|
|
Whilst we do not know how the astronomers could have predicted eclipses at that time, we learn from the 'Chou
|
|
pi' of the 'Kai-T'ien' model of the motion of the sun [2]. The 'Chou pi' probably dates from about 1100 B.C., but it is possible that the cosmological model was a later addition either indigenous to China or imported from India where a very similar model is described in the Suryapi-ajnapti (circa 500 B.C.) [3]. The model has the sun describing a set of seven circles about the celestial pole at a height of 80,000 li above a flat earth; the innermost circle has a diameter of 238,000 li, the outermost circle a diameter of 476,000 li. The sun moves on the
|
|
inner circle at summer solstice and moves from circle to circle during the course of six months until at winter sol-
|
|
|
|
stice it is on the outermost circle. The sun's rays only extend a distance of 167,000 li so explaining night and
|
|
day.
|
|
This model is quite good. Indeed, one can compute that at a latitude of 36° the model correctly predicts the elevation angles of the sun at noon on both midsummer's and midwinter's day. But is it Science? Indeed, what is
|
|
Science?
|
|
The ancient Chinese were clearly aware of the regularity of the motion of the sun across the sky and of the seasons. They constructed a model based on these observations, the model explained past observations (at least to some level of accuracy) and successfully predicted future observations. What more do we require before giving such a model the accolade of being scientific? Is not this model as scientific as Kepler's Laws?
|
|
The ancient Chinese scientists had made that first step
|
|
in science of beheving that the future could be predicted
|
|
on the basis of past experience. This is the act of faith we make in science although as pointed out by Hume, it is an act of faith and we cannot on the basis of past experience
|
|
prove that our predictions will be true in the future [4]. The Chinese model was quantitative and not just qualitative. It was narrow, applying only to one set of
|
|
phenomena, so it lacked the generality we associate \nth scientific reasoning. But I nevertheless think we should
|
|
describe these Chinese atronomers as early scientists.
|
|
2. Geometry as an Example of Science
|
|
A better example of early science is geometry. The ori-
|
|
gins of geometrical knowledge also go veiy far back in the history of mankind; some special laws such as
|
|
Pythagoras' Theorem in the form 6- + 8- 10- were known to the Chinese. The fact that the circumference of a circle is a constant multiple of its diameter was also
|
|
|
|
1
|
|
|
|
known to several ancient civilizations, as v^^as the existence of similar triangles. However, the main body of geometrical knowledge was accumulated by the Greeks
|
|
and it is to this culture that I turn for my discussion on
|
|
geometry as a science.
|
|
|
|
Let us take a few simple geometrical results and ask what they tell us about the world. Three such examples
|
|
|
|
are:
|
|
(a) The sum of the angles of any triangle equals two
|
|
|
|
right angles.
|
|
(b) In a right angled triangle the sum of the squares of the lengths of the two smallest sides equals the
|
|
square of the length of the hypotenuse.
|
|
|
|
(c) The circumference of any circle is a constant mul-
|
|
tiple of its diameter.
|
|
|
|
These results can properly be considered as laws of na-
|
|
|
|
ture. They are found experimentally by drawing trian-
|
|
|
|
gles and circles and measuring lengths and angles. They
|
|
|
|
tell us quite a lot about the world we live in: The results
|
|
|
|
are the same no matter where we carry out the experi-
|
|
|
|
ments; the laws are true for all orientations of triangles;
|
|
|
|
they were true in 400 B.C. and are true today; in order
|
|
|
|
to conduct such experiments we need to define standards
|
|
|
|
and measuring procedures
|
|
|
|
These laws are
|
|
|
|
general, that is when stating them we are not only say-
|
|
|
|
ing that these laws were satisfied for all triangles and
|
|
|
|
circles that have been measured, but that they are true
|
|
|
|
We for all triangles and circles.
|
|
|
|
have made that inductive
|
|
|
|
leap from the particular to the general that is charac-
|
|
|
|
teristic of science and are prepared to use these laws to
|
|
|
|
predict the outcome of future experiments. In doing so
|
|
|
|
the ancient Greeks were accepting that nature satisfies
|
|
|
|
' laws of nature' that can be uncovered by experiment.
|
|
|
|
But the contribution of the Greeks does not stop at the discovery of such laws. Their main contribution to geometry was to recognize that all these empirical laws could be deduced from a small set of fundamental laws: the axioms of Euclidean geometry together with definitions of the objects that enter those laws and the rules of logic that we use in deductive reasoning. Examples of these latter two categories are [5]:
|
|
A straight line is a Hne which lies evenly with the
|
|
points on itself.
|
|
|
|
Things which are equal to the same thing are equal to each other.
|
|
|
|
The axioms or fundamental laws as defined by Euclid are
|
|
|
|
[5]: (1)
|
|
|
|
It is possible to draw a straight line from any point to any point.
|
|
|
|
(2) It is possible to extend a finite straight line continuously in a straight line.
|
|
|
|
(3) It is possible to describe a circle with any center and any radms.
|
|
|
|
(4) All right angles are equal to one another.
|
|
|
|
(5) If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
|
|
|
|
These fundamental laws clearly represent an extrapola-
|
|
|
|
tion from experience. Our experience is finite. Within
|
|
|
|
this finite domain we find these laws to be satisfied (to
|
|
|
|
some level of accuracy!) so we postulate that they can be
|
|
|
|
generalized to the above. Given these fundamental laws
|
|
|
|
all the other laws of geometry can be deduced by logical
|
|
|
|
(i.e., mathematical) reasoning. This is just what we try
|
|
|
|
We to do in modern physics.
|
|
|
|
find laws applicable to dif-
|
|
|
|
ferent sets of phenomena and then seek more fundamental laws from which this variety of subsidiary laws can be
|
|
deduced.
|
|
3. The First Constant of Nature?
|
|
Let me return to one of the early geometrical laws:
|
|
"The circumference of any circle is a constant multiple of the diameter."
|
|
What is this constant multiple, and how can it be determined? The multiple is given the label -tt and we determine it by measurement. If I take a circle and some measuring device, for example my wife's tape measure
|
|
(borrowed from her sewdng box!) I can first of all test that it is a circle by measuring the diameter at different orientations. I always find the same value, say 8 inches. I then measure the circumference and find that it is say
|
|
25 inches. The ratio is -tt = 25/8 = 3.125. I repeat the experiment in London and in Washington, and I find more or less the same answer. I do the same experiment with different size circles and I find more or less the same answer. I have therefore determined the first known constant of nature as tt = 3.125.
|
|
Such a simple experiment raises several interesting questions: First one might ask about the measuring ap-
|
|
paratus. A plastic tape measure is not perhaps the most
|
|
accurate of measuring rods and I doubt if it would compare very favorable with the standard definition of length whether by reference to the old standard meter or
|
|
to the new standard using the velocity of light. Yet it has some advantages. I can fold it back on itself and compare
|
|
the one inch intervals on one part of the tape with those on another part; they seem to agree. Thus the subdivi-
|
|
sions may not be equal to a standard inch but they are
|
|
equal to each other. But since the value of tt is given by the ratio of the circumference to the diameter it does not
|
|
matter whether the scale on my measure agrees with the
|
|
standard or not; the ratio of lengths and therefore the value I find for tt is only dependent on an accurate divi-
|
|
sion of my measuring tape. This independence of the de-
|
|
finition of a measuring standard is not confined to the determination of tt; the fine structure constant, or the ratio of proton to electron masses are pure numbers and therefore independent of the standard units of mass, length, charge, or time. Units are only an intermediary that enable us to attach labels of mass, length, etc., to other quantities, but the constants of nature are really pure numbers, independent of units. This is a point I will return to later on in this article.
|
|
Again this simple experiment can teach us something about experimental procedures. If I repeat the experiment at different times on circles of different dimensions and at different places I do not get exactly the same result, only 'more or less' the same result. Thus a se-
|
|
quence of five measurements may give the values
|
|
3.125 3.163 3.142 3.120 3.157
|
|
I now recognize that one measurement does not give an exact result so I take an average and obtain tt = 3.1414, and believe that this is a more accurate estimate of tt.
|
|
Indeed, if I follow the standard practice of estimating the uncertainty to be attached to this value I would then calculate the standard deviation to be 0.01695 and give the experimental determination of tt as
|
|
TT - 3.141 ± 0.017.
|
|
It is important to realize that in following the above
|
|
procedure I have made an act of faith, namely that there
|
|
|
|
2
|
|
|
|
is a unique value of it that can be determined to some accuracy by taking many measurements. I have ruled out the possibility that it is really a stochastic quantity and
|
|
that my measurements reflect such a fact about nature. On the basis of my experimental determination of I
|
|
cannot justify such an assumption. The same problem necessarily arises with all measurements, for example, why should not the fine structure constant be a stochastic quantity? It is true that past experience shows that as we make more accurate experiments the latest determinations do not show the earlier fluctuations so we deduce that these earlier fluctuations were experimental error. But if we then claim that this experience proves the
|
|
present set of values do not reflect the stochastic nature
|
|
of the world, we are again up against Hume's argument that we cannot prove that our laws will hold true in the
|
|
future just because they held good in the past.
|
|
Of course if we now wish to evaluate -n- we would not do it by an experiment of the kind I described; we would calculate it mathematically. For example we might use the power series for tan'^x obtained from the integral
|
|
obtained by Newton, Leibniz, and Gregory [6]:
|
|
|
|
tan
|
|
•^0 1+2/2
|
|
|
|
-I-
|
|
|
|
S
|
|
|
|
^
|
|
|
|
7
|
|
|
|
Taking x - 1 gives the Leibniz expression [6]
|
|
|
|
- =1-1 + 1-1 + 1
|
|
|
|
4
|
|
|
|
3
|
|
|
|
5
|
|
|
|
7
|
|
|
|
9
|
|
|
|
This result, though elegant in relating tt to simple frac-
|
|
|
|
A tions, is of no practical use.
|
|
|
|
much better formula is
|
|
|
|
that obtained by Machin [7] which is
|
|
|
|
i=4ta„-'i-ta„-'^
|
|
|
|
=4 1
|
|
5
|
|
|
|
1 J_
|
|
3 53
|
|
|
|
1 J_
|
|
5 5^
|
|
|
|
1
|
|
239
|
|
|
|
11+ .
|
|
3 2393
|
|
|
|
1 J_
|
|
7 5^
|
|
|
|
9 5^
|
|
|
|
Thus IT can be determined to any required accuracy; it is no longer a constant of physics but a constant of mathematics! What does this mean? If a physical constant Hke the ratio of the circumference to the diameter of a circle can be determined by mathematics, why not
|
|
other physical constants like the fine structure constant,
|
|
the mass ratios of elementary particles .... Is physics reducible to mathematics?
|
|
4. The Relationship Between IVIathematics and Physics
|
|
The mathematical reasoning that led to the power series for tan^a; and hence for tt is part of Euclidean geometry; that is, provided the fundamental laws, or Euclid's axioms, are true, then the ratio of the circumference of a circle to its diameter is calculable from the above series. But what does it mean to ask if the axioms of a branch of mathematics are true? All that we ask in mathematics is that the axioms be consistent, that is they do not lead to contradictory conclusions. Mathemat-
|
|
ics is not true or false, it is simply a procedure for deduc-
|
|
ing the consequences of a particular set of axioms. What we are doing is to ask whether the axiom set of Eu-
|
|
clidean geometry is an appropriate mathematical model for the physical world, so that the theorems of Euclidean geometry can be taken over into statements about physical geometry. This clearly requires us to define the ob-
|
|
|
|
jects we call lines and angles in a physical way. Whether
|
|
these definitions then satisfy the axioms of Euclidean geometry is an empirical question that can only be settled by experiment.
|
|
|
|
There are several definitions of a straight line that conform to everyday concepts. One is the path of a light ray. Indeed, it is possible that this is what was behind Euchd's statement that "a straight line is a line which lies evenly with the points on itself" but it is not the only definition. Another is the geodesic definition that a straight line is the shortest distance between two points; that is, of all the possible paths joining two points the straight line is that which requires the minimum number of measuring rods laid end to end to cover the distance
|
|
from one point to another. A right angle can be defined
|
|
as one quarter of a revolution such that four such angles
|
|
which coincide when laid one on top of another constitute a complete revolution when laid side by side. An alternative definition is that it is the angle between two straight
|
|
lines such that the distance from a point on one line to a point on the other is a minimum. Wliether these alternative definitions are equivalent is again an empirical issue, and having chosen one definition it is again an empirical issue as to whether these physical definitions have the same properties as the lines and angles in Euclidean
|
|
geometry. Of course we can only verify that they do to a
|
|
certain level of accuracy, so whilst our mathematical
|
|
deductions from the axioms are correct we cannot be
|
|
sure that they correspond to consequences for the physi-
|
|
|
|
cal behavior of objects.
|
|
|
|
There is a philosophical point here of some substance as was emphasized by Poincare [8]. Suppose we found that our physical geometry did not agree with Euclidean
|
|
geometry. How are we to interpret such a finding? One
|
|
possible route is to stick to our definition of a straight line as, say, the path of a light ray, in which case the
|
|
geometry of light rays is non-Euclidean. On the other hand we could say that light does not follow straight lines since they do not satisfy Euclidean geometry. The
|
|
physicist would then seek to explain this departure from Euclidean geometry by saying that light rays are bent by the presence of other objects in the universe. Within present day science the situation is somewhat confused.
|
|
On the one hand we talk about geodesies and curved
|
|
— space on the other hand we talk about the bending of
|
|
light, that is bending compared to a EucHdean straight
|
|
line. This illustrates Poincare's conventionality thesis, subsequently elaborated by Reichenbach and other phi-
|
|
losophers of science, that there are many ways of inter-
|
|
preting a given physical situation depending on the definitions used. Contrary to oft repeated claims, there is no information conveyed in the statement "space is non Euclidean." Our knowledge is of the behavior of objects,
|
|
not space. It may be convenient to talk of light as defin-
|
|
ing straight hnes and that the light geometry is non Euclidean, but it is no more (or less) correct than to claim the straight Hnes are those that satisfy Euclidean geometry and that light rays are bent.
|
|
|
|
Yet another lesson to be learnt from geometry is that
|
|
|
|
there is no clear division between what we consider as
|
|
|
|
axioms or fundamental laws, and what we consider as
|
|
|
|
theorems or deductions from those laws. For example,
|
|
|
|
the axioms of Euclid can be used to prove Pythagoras'
|
|
|
|
theorem, or alternatively, Pythagoras' theorem can be
|
|
|
|
taken as the fifth axiom and then the statement that
|
|
|
|
straight lines meet if produced indefinitely becomes a
|
|
|
|
theorem. Alternatively, the fifth axiom could be taken to
|
|
|
|
be the statement that similar triangles exist, or the sum
|
|
|
|
of the angles of a triangle is half a revolution
|
|
|
|
One
|
|
|
|
3
|
|
|
|
man's axiom is another man's theorem! So it is in the
|
|
other branches of science; we choose to take particular
|
|
statements as fundamental laws and others as deductions from those laws but laws and consequences can be inter-
|
|
changed and we have no way of establishing one set of
|
|
laws as 'the laws of nature'.
|
|
5. The Truth of Euclidean Geometry
|
|
Even in Greek times there was some unease about the fifth axiom and attempts were made either to replace it by some more self-evidently true axiom or to deduce it from the other four. The best known attempt was by Ptolomy who tried to deduce the parallel axiom from the
|
|
first four of Euclid's axioms together with the first twenty eight theorems derived by Euclid which are independent of the fifth axiom, but in this as in other attempts some other assertion entered the argument and effectively replaced the fifth axiom.
|
|
However, there does not seem to have been much doubt that Euclidean geometry was indeed the physical geometry of the world. Indeed, it was so firmly held to
|
|
be true that attempts to demonstrate the validity of other branches of mathematics used the model of Euclidean geometry. Almost all philosophers, mathematicians, and scientists held Euclidean geometry to be necessarily true. Isaac Barrow (Newton's predecessor at Cambridge) held that this truth was derived from innate reason. Newton, Leibniz, Lock, and Hobbes held that Euclidean geometry was inherent in the design of the
|
|
universe. One notable exception was David Hume, to
|
|
whose ideas I have already drawn attention. Hume ar-
|
|
gued both against the necessity of laws and contended that no amount of past experience could demonstrate that the future vdll obey such laws; knowledge is empirical and the laws of Euclidean geometry, like other laws, are not necessary truths.
|
|
On the other hand Immanuel Kant maintained that Eu-
|
|
clidean geometry is an a priori synthetic truth, that is (roughly interpreted) that our minds compel us to organize our experiences around certain intuitions of space and time and that Euclidean geometry was one such a priori synthetic truth. So pervasive was Kantian philosophy that even when Gauss had convinced himself that nonEuclidean geometry was possible he states in a letter to Bessel that he would not pubHsh his findings because he
|
|
feared ridicule.
|
|
As with many of the discoveries of science and
|
|
mathematics there is no one person that can be called the discoverer of non-Euclidean geometry. Lambert reached
|
|
the conclusion that there could be many geometries derived from different axioms but it was Gauss who
|
|
recognized that the non-Euclidean geometry could apply to the physical world; in a letter to Olbers written in
|
|
1817 he concluded [9] "... we must place geometry not in the same class as arithmetic which is purely a priori
|
|
but with mechanics ..."
|
|
This empirical approach to geometry led to Gauss surveying a triangle formed by the mountain peaks Brocken, Hohenhagen, and Inselsberg to determine the sum of the angles of a triangle [10]. In fact the result obtained was 180° 14.85" but Gauss realized that the error exceeded 14.85" so that the correct result could have been 180° or
|
|
less, and that it was any way unlikely that we could find
|
|
a positive result with such a small triangle (the sides were 69, 85, and 197 km). However, at least the distinc-
|
|
|
|
tion had been made between physical and mathematical
|
|
knowledge.^
|
|
|
|
6. Newtonian Gravitation and Mechanics
|
|
|
|
I now wish to examine the laws of mechanics and gravitation by which Newton and his successors were able to
|
|
account for the motion of planets, the rate of pendula
|
|
clocks, the motion of projectiles . . . According to
|
|
Newton's laws the motion of a body of mass mi under the gravitational attraction of a second body of mass mz
|
|
is given by [11]
|
|
|
|
dhi2 _ -G(mi + mi)
|
|
|
|
~]72
|
|
|
|
3
|
|
|
|
where ri2 is the (vector) distance between the two masses, G
|
|
is the Newtonian constant of gravitation, a universal constant of nature to be determined by experiment [11].
|
|
G This constant is of a different kind to tt. It has di-
|
|
mensions and therefore its value depends on the units in which it is measured. The quantity tt on the other hand is a pure number; its value is unit independent. This should
|
|
make us ask what is meant by calling G a constant of
|
|
nature.
|
|
|
|
Let us examine carefully the content of Newton's law.
|
|
|
|
m It contains the symbols r for length, t for time,
|
|
|
|
for
|
|
|
|
mass. What do these symbols mean? How are mass,
|
|
|
|
length, and time to be measured?
|
|
|
|
Firstly, the laws only apply in an 'inertial frame', that is in a system of reference in which freely moving parti-
|
|
cles continue with constant velocity. Yet to know whether particles have a constant velocity presupposes a measure of time and distance! Suppose we use a rigid rod
|
|
to measure distance. We can now define a measure of
|
|
inertial time such that a freely moving particle covers equal distances in what we define as equal times. This
|
|
particle, of course, necessarily covers equal distances in equal times. It then becomes a matter of empirical investigation as to whether other particles also cover equal distances in equal times as measured by that inertial clock; Newtonian mechanics is based on the hypothesis that such frames of reference do exist in nature. In prac-
|
|
tice time was not measured using freely moving particles, but either by the rotation of the earth around its axis, or some gravitational clock such as a pendulum. Do these clocks keep Newtonian inertial time?
|
|
|
|
It is an elementary deduction from Newton's laws that
|
|
the total angular momentum of an isolated system of in-
|
|
teracting particles does not change in inertial time. Thus the angular velocity of a rigid body is constant in inertial
|
|
time so the rotation of the earth provides a tolerably good clock. However, it is not self evident that Nevi1:on's
|
|
laws are true. We could imagine a world in which the an-
|
|
gular momentum of an 'isolated' body changed (slowly) as measured in inertial time. Whether or not this is the
|
|
case is an empiiical question.
|
|
A pendulum clock is a gravitational rather than an
|
|
inertial clock, as is the motion of the moon around the earth, the earth around the sun, etc.; these depend on
|
|
the law of gravitation as well as the laws of motion. Newton's law of gravity is not self evidently true and
|
|
|
|
As far as I am awai'e, no one has proposed an improved version of Gauss' experiment; for 3 satellites in orbit around the earth the sum of the
|
|
angles according to general relativity would be 180° plus an excess of about 0.005".
|
|
|
|
4
|
|
|
|
needs to be tested: is the symbol t that enters the law of
|
|
|
|
gravity the same as inertial time? Is the constant of
|
|
|
|
gravity, G, really a constant in time and/or space? These
|
|
|
|
are empirical questions that can only be decided by ex-
|
|
|
|
periment. Such conceptually simple experiments would
|
|
|
|
compare the period of a pendulum, or the length of the
|
|
|
|
year with the length of a day. Suppose Newton's law of
|
|
|
|
gravity is true for some time scale tg. The period of a
|
|
|
|
pendulum P^, and the length of the year
|
|
|
|
would then
|
|
|
|
be
|
|
|
|
1/2
|
|
|
|
M^
|
|
|
|
M 1
|
|
G y2
|
|
|
|
Pk = 27: Ll^ 1/2
|
|
|
|
' 1/2
|
|
|
|
Me where I is the length of the pendulum,
|
|
|
|
the mass and
|
|
|
|
the radius of the earth, Le the radius of the earth's
|
|
|
|
Mq orbit around the sun, and
|
|
|
|
the solar mass. If Pc and
|
|
|
|
Pe varied in time (as measured by an inertial clock) we could interpret this as the constant of gravity G = G{t).
|
|
However, this would require P e /P c to be independent of
|
|
time since they are both gravitational clocks. If P^/Pq
|
|
|
|
varied in time then we would require a spatial as well as
|
|
|
|
temporal variation in G.
|
|
|
|
So far I have paid little attention to the meaning of the
|
|
m symbols r for length and for mass. Within Newtonian
|
|
mechanics we measure length by two means, rigid rulers,
|
|
and triangulation. It is an empirical fact about the world that objects that are the same length at one place remain
|
|
equal in length when transported to another place. We
|
|
can therefore usefully base our measurement of length on
|
|
such a basis. We cannot however test that bodies do not
|
|
change in length when transported, so it is purely a convention to assume that they do not. The triangulation method of length measurement is based on the assertion
|
|
that Euclidean geometry is valid both for rigid bodies and for the path of light rays. As I pointed out earlier,
|
|
whether or not these assertions are true are empirical
|
|
questions.
|
|
|
|
The mass that enters Newton's laws is the inertial
|
|
mass defined in terms of momentum conservation. Having set up a measure of length and time we can choose one standard mass mo. By measuring initial and final velocity in a collision experiment we determine the iner-
|
|
M tial mass of another body through the relation
|
|
|
|
mo
|
|
|
|
u\
|
|
|
|
+
|
|
|
|
MU \
|
|
|
|
=
|
|
|
|
mo
|
|
|
|
U{
|
|
|
|
+
|
|
|
|
MUj,
|
|
|
|
UO U where {Ui,
|
|
|
|
and {U{,
|
|
|
|
f) are the initial and final velo-
|
|
|
|
cities of mo and M. Any one such experiment gives a
|
|
|
|
value for M. The empirical content in the law of momen-
|
|
|
|
tum conservation is that any initial conditions (Ui, U\)
|
|
M give the same value of for a given object. Newton's
|
|
|
|
law of gravity states that the source of the gravitational
|
|
|
|
field is proportional to the inertial mass, or that the con-
|
|
|
|
stant of gravity, G, is actually a constant independent of
|
|
|
|
the nature of the bodies.
|
|
|
|
7. The Newtonian Constant of Gravity
|
|
|
|
Having laid down a procedure for measuring mass, length, and time we can now ask what meaning can be
|
|
|
|
given to the constant of gravity within mechanics and
|
|
gravitation. The basic units are arbitrary; let us call
|
|
them mo, Iq, to. We can now imagine an experiment to
|
|
determine G by measuring the period of a pendulum of length L = Ni Iq, on the surface of a planet of mass
|
|
M = Nz mo, whose radius is R - N'^ Iq; ii the period
|
|
N P - i toVfe have
|
|
|
|
3
|
|
|
|
G = 4tt2
|
|
|
|
1''0
|
|
|
|
mo
|
|
|
|
Nj_Nj_
|
|
N2 Ni
|
|
|
|
N Clearly A^i, 2, N3,
|
|
|
|
are measurable (by counting)
|
|
|
|
so G can be determined in units of mo, lo, and to. More-
|
|
|
|
over we could imagine a world in which this experiment
|
|
|
|
would give a different value of AT 4 and hence of G
|
|
|
|
depending on position and time. It is therefore meaning-
|
|
|
|
ful to talk about a variation of the constant of gravity
|
|
|
|
within the framework of Newtonian mechanics.
|
|
|
|
If we also introduce the velocity of light, c, we can
|
|
|
|
compare a gravitational clock with a light clock. For ex-
|
|
|
|
ample we could imagine an experiment in which two bod-
|
|
|
|
ies were in orbit about each other and reflected a light
|
|
|
|
signal back and forth. The number of such round trip sig-
|
|
|
|
nals in one orbit (relative to an inertial frame) is a
|
|
|
|
measurable; it could be constant in time or vary in time.
|
|
Similarly, given our choice of standards Iq, to, we can
|
|
measure the velocity of light c. This could be constant or
|
|
|
|
varying as measured in inertial time. Indeed, we could imagine a world in which both c and G varied in inertial
|
|
|
|
time and in which the number of round trip light signals
|
|
|
|
in a gravitational orbit also varied.
|
|
|
|
While we can imagine a world in which c - c{t),
|
|
G = Git), what would it mean to say that G were constant but different in value? How would this manifest itself in measurable ways? To say that G ^ Git ) we mean
|
|
that having chosen our units mo, lo, to, we find a different result of a given experiment when done at dif-
|
|
|
|
ferent times but referred to the same units. But we can-
|
|
|
|
not transport our arbitrary units mo, ^o. ^0 from this world to some other I might imagine. The problem is that
|
|
|
|
the world of Newtonian mechanics is continuous. There
|
|
|
|
are no intrinsic standards of mass, length, and time de-
|
|
|
|
fined within the system so that measurement cannot be
|
|
entirely reduced to counting and I cannot compare my
|
|
|
|
two worlds. Within Newtonian mechanics the value of G
|
|
|
|
is meaningless; it just reflects the arbitrariness of our
|
|
|
|
choice of units. For illustration let us imagine that with
|
|
|
|
the standard pre-atomic definitions of kilogram, meter,
|
|
|
|
and second, we found that
|
|
|
|
G = 6.67 X 10"
|
|
|
|
kg"
|
|
|
|
The relative behavior of the moon and planets would be unchanged. The only change would be in the number of days in a year, and the number of swings of a 1 meter pendulum in one day; that is, comparisons of gravitational phenomena with our arbitrarily defined inertial clock. The observed phenomena could be equally explained by stating that the earth was spinning ten times faster so that there were only 8640 seconds in a day and G had its usual value.
|
|
This should be contrasted with a world model with discrete intrinsic structure. For example, if all bodies were
|
|
m made up of a basic unit 0 of radius / 0, by using the propaga-
|
|
tion of light 1 0 can also be a unit of time 1 0, and all measure-
|
|
ments are now reducible to counting. In terms of these basic units G is a number; if it had a different value physics would be different. For example the period of rotation of the earth is some pure number times the intrinsic unit <o so I can
|
|
meaningfully state that the rotation rate is different and so
|
|
separate a change in the earth' s rotation from a change in G. Since our present models of the world do have a discrete
|
|
quantized structure, an absolute determination of G be-
|
|
comes meaningful.
|
|
|
|
8. Quantum Clocl(s
|
|
|
|
The previous discussion is somewhat removed from actual practice. Time and distance standards are normally based on quantum phenomena and the properties of light. Electric charge apparently comes in identical 'lumps", in-
|
|
|
|
5
|
|
|
|
teger multiples of the charge on an electron e (or possibly multiples of e/3?). Matter also comes in lumps, m^, m^,
|
|
etc., and angular momentum comes in multiples of n.
|
|
This allows us to define an atomic unit of time, for example the period of revolution of an electron in the ground state of a hydrogen atom as
|
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|
|
^0
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|
4
|
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|
,
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|
|
and a unit of length, Yq, as the radius of this orbit:
|
|
|
|
We can now measure time in units of Pq, length in
|
|
units of ro, and mass in units of m^. If Newton's laws are
|
|
true the period Pe of the earth around the sun is given
|
|
by
|
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|
|
u
|
|
E
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|
f
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|
o
|
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|
1 1/2 f
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|
1 1/2 f ^ -] 1/2
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|
Po
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|
Gnil
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|
Mo
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|
Each term in parentheses is a pure number and therefore
|
|
represents at least in principle an empirical measure-
|
|
ment. Thus we can meaningfully ask if this relation is
|
|
satisfied (i.e., is Newton's law true in atomic units) and
|
|
determine the value of G by determining the dimension-
|
|
less number e^/Gmi. We can also meaningfully ask if this
|
|
dimensionless number (=10^^) is constant in time, that is do we get the same value when we conduct an experi-
|
|
ment at different times? We should, however, remember
|
|
that should we find a time variation we have a choice between saying e and m^, are constant in time and G varies, or taking G to be constant and letting e and/or
|
|
vary in time.
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|
9. The Fine-Structure Constant and Other Numbers
|
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|
So far we have not considered the velocity of light.
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|
Since we have a quantum definition of length and time it
|
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|
|
is now an empirical question as to whether the velocity of
|
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|
light is constant as measured in these quantum units. For
|
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|
example, the time required for a light signal to travel a
|
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|
distance
|
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|
|
measured in units of Pq is
|
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|
2-nf 0
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|
cPi
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|
1ic
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|
|
|
which is the fine-structure constant. Whether or not a is
|
|
constant in time is therefore an empirical result about the world, and this can only be settled by experiment.
|
|
Similarly, we may ask if the mass ratio of elementary
|
|
particles, i.e., m^/nig, varies in time. Indeed, any pure number is independent of our choice of units and can be considered as a possible candidate for time variation. In the end it is experiment that has to decide; all philosophy can do is to try and separate the meaningless from the meaningful questions.
|
|
One might reasonably ask why we should expect any time variation of numerical constants. To answer this we must consider the large scale structure of the universe.
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|
10. Cosmology
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|
There are very few measured properties of the large scale structure of the universe, and even fewer that have any claim to accuracy. The best known is probably the Hubble parameter Hq. This is often thought of as the
|
|
constant of proportionality in the velocity-distance rela-
|
|
tion for the expanding universe, V = H^r. However,
|
|
|
|
distances and velocities are inferred quantities; the actual measurables are the energy per unit time per unit area F, and the red shift Z, of light from distant galax-
|
|
ies; Ho is then calculated from the relation
|
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|
F=
|
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|
|
[1 + (go - 1)Z + ...]
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|
|
where L is the intrinsic luminosity of such galaxies. Estimates of L and hence Ho vary by factors of one to four (and maybe more). Consequently Ho is only known to a factor of about 2 (or more!); to order of magnitude Hq^ —
|
|
10^^ years.
|
|
|
|
The parameter go in the above expression is called the deceleration parameter and is related to the rate of change of the Hubble constant Ho- One of the challenging problems of observational cosmology is to determine the actual value of go since (with the aid of some theory!) it" will tell us whether the universe will continue to expand or contract. If the mean density of matter in the
|
|
universe, po, can also be determined, these parameters will tell us whether our simple cosmological models are
|
|
|
|
valid.
|
|
|
|
This mean density, po, is difficult to estimate. If we just estimate the masses of galaxies then po — O.Olpc
|
|
where pc is called the critical density and is such that
|
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|
|
1
|
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|
|
=1
|
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|
|
S H^
|
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|
|
2-
|
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|
|
But of course there may be mass that we have not yet
|
|
|
|
detected; halos of galaxies, matter in intergalactic space
|
|
|
|
(e.g., bricks!), dead stars, black holes, massive neutri-
|
|
|
|
nos, gravitational waves
|
|
|
|
As I said earlier there
|
|
|
|
are few reliable measurements in cosmology!
|
|
|
|
11. Dimensionless Constants of Nature
|
|
The two cosmological parameters. Ho and po, can be
|
|
combined with other constants of nature, G, c, e, and m^, to give the following pure numbers:
|
|
|
|
6 X 10,40
|
|
|
|
4 X 10'"';
|
|
|
|
= 4 X 1042
|
|
GfUf
|
|
The first parameter is often referred to as the age of the
|
|
universe in atomic units; the second is the ratio of atomic to cosmological density; and the third is the ratio of electrical to gravitational forces. Other pure numbers
|
|
we have considered are the fine-structure constant and the mass ratio of the electron to proton:
|
|
|
|
a—
|
|
1ic
|
|
|
|
1
|
|
137'
|
|
|
|
1
|
|
1836
|
|
|
|
Why do these numbers have these values? Why is the
|
|
ratio of the circumference to radius of a circle equal to
|
|
3.1415926. . .? Can these numbers be deduced from a single theory such that no other values are possible? Are these numbers just random initial conditions for the universe? What would the universe be Hke if these numbers were different?
|
|
|
|
I think most scientists would conjecture that one day
|
|
|
|
we will be able to explain why the particle masses are as
|
|
|
|
observed, and why the fine-structure constant has its
|
|
|
|
particular value. At the moment we do not have a deep
|
|
|
|
enough understanding of particle physics to provide the
|
|
|
|
A explanation.
|
|
|
|
similar view can be taken about the
|
|
|
|
cosmological numbers of the order of 10^". Such funda-
|
|
|
|
mental theories linking cosmology and microphysics have
|
|
|
|
6
|
|
|
|
been pursued by several people, but without apparent success [12, 13]. The point of view of Dirac [14] is that whatever the theory is, it will entail that where such large numbers as 10^° occur, then parameters of this magnitude are proportional to each other, so that
|
|
|
|
Gm'i " e^Ho
|
|
where ki and k2 are of order unity. This statement is
|
|
known as The Large Number Hypothesis.
|
|
|
|
I should point out that the standard, general relativistic cosmological model does not satisfy this hypothesis; the first parameter is constant in time, the second parameter varies linearly vdth time, and the third
|
|
|
|
parameter varies with the square of the time. (These
|
|
|
|
statements are only strictly true for the Einstein-de
|
|
|
|
Sitter model.) It is therefore pure accident that, these three numbers happen to have approximately the same
|
|
|
|
value at the present time.
|
|
|
|
The large number hypothesis leads to the result that
|
|
|
|
either all three parameters are constant in time, or they vary in unison. The first proposal leads directly to the
|
|
|
|
steady state cosmology in which G, Ho, and po are constant. This in turn implies the creation of matter [15]. The steady state theory has few advocates these days as
|
|
|
|
its very specific predictions are apparently contradicted
|
|
|
|
by observation, for example, the radio source counts. I
|
|
must admit that I am not wholly convinced that some
|
|
form of the steady state theory cannot stand up to this
|
|
|
|
data, for example, a statistically steady state with local
|
|
|
|
fluctuations.
|
|
H The second proposal advanced by Dirac is that as
|
|
is a time, related to the age of the universe, then we
|
|
|
|
should find
|
|
|
|
H,
|
|
|
|
1
|
|
|
|
Po
|
|
|
|
This is one origin of the idea that the Newtonian constant of gravity varies in time, although this proposal was advanced somewhat earlier by E. A. Milne [16]. Such a variation is incompatible with general relativity and some new theory needs to be advanced that successfully explains this time variation, and whose predictions can be evaluated and subjected to empirical investigation. The scalar-tensor theory of Brans and Dicke [17] was such an
|
|
attempt, but it cannot successfully explain the time vari-
|
|
ation of G and po [18]. I have considered many other pos-
|
|
sible theories but I have not, as yet, been able to find one that explains all the large number relations and agrees with solar system tests on the orbits of planets
|
|
|
|
[19].
|
|
|
|
Recently Dirac introduced a two metric framework. In
|
|
|
|
the gravitational metric, dSg, Einstein's equations are
|
|
valid, and this is conformally related to an atomic metric,
|
|
dsA = dSg/p, where p is to be determined [20]. Without any theory for the determination of p all that can be done is to ask general questions such as what classes of theory satisfy the large number hypothesis [21] and what consequences would such theories have in other branches of
|
|
physics [22]. My own view is that little progress can be
|
|
made without some more precise theory.
|
|
|
|
However, experimentally there is clearly a testable
|
|
|
|
prediction, namely that the constant of gravity G decreases in atomic time, G/G — -10^^ years. This can be
|
|
|
|
tested either by radar ranging experiments or by labora-
|
|
|
|
A tory tests.
|
|
|
|
second prediction is that there could be
|
|
|
|
creation of matter proportional to matter already
|
|
|
|
present, and this might be detectable in the laboratory
|
|
|
|
[23]. At the present time no experiments are sensitive
|
|
|
|
enough to detect these effects.
|
|
|
|
12. The Anthropic Principle
|
|
|
|
I have already pointed out that in standard theory (i.e. general relativity and quantum mechanics) the large numbers vary in time, and it is just a chance event that these three numbers happen to be about 10""^. These numbers could be different, in which case the properties of the universe would be different, and in particular we,
|
|
man the observer, would not be here to ask why the
|
|
universe is as it is. This idea has been elevated to the status of The Anthropic Principle [24, 25, 26].
|
|
|
|
Since man contains heavy elements there must have
|
|
been nucleosynthesis, therefore there must have beerstars that have evolved to supernovae and ejected heavy
|
|
elements into the interstellar material. This material
|
|
then formed other stars with planets on which life as we know it evolved.
|
|
A star is an object in which pressure balances gravity
|
|
and in which gas pressure dominates over radiation pressure; this is sufficient to show that stars have masses up
|
|
to a maximum Mq where
|
|
|
|
Mi _ nip
|
|
|
|
Gm2
|
|
and an - ^ ^
|
|
nc
|
|
|
|
On the other hand the central temperature must be high
|
|
enough for nuclear reactions to take place before the gas is degenerate. This gives a minimum mass of about 0.01 Mq. The luminosity of a star is essentially determined by radiative energy transport. The principal opacity source is scattering by electrons, and this permits the evaluation of the luminosity Lq. The evolution time for a star is essentially the time to convert a significant fraction of hydrogen to helium and so is proportional to Mq/Lq. The
|
|
actual result gives
|
|
|
|
1
|
|
|
|
evol
|
|
|
|
•
|
|
o-G mpC 2
|
|
|
|
The anthropic principle is now used to argue that if the age of the universe Hq^ is less than ^evoi then no stars would have evolved. On the other hand, if the universe is very much older than t^voi there would be no stars left. Conditions are therefore ripe for Hfe to develop when the
|
|
universe is just a little older than ^evoi or
|
|
|
|
_1 J_ n
|
|
|
|
Hq
|
|
|
|
olq ninC^
|
|
|
|
rtipC^
|
|
e^Ho
|
|
|
|
1
|
|
Gm^
|
|
|
|
where a is the fine-structure constant. This 'explains'
|
|
why this large number coincidence is observed.
|
|
|
|
The second large number coincidence is 'explained' by
|
|
|
|
appealing to cosmological models. In such general rela-
|
|
|
|
tivistic models the deceleration parameter go is
|
|
|
|
go = 4tt
|
|
S
|
|
|
|
G Po H§
|
|
|
|
In the Einstein de Sitter model qo ^ 1/2. If 90 were very much less than 1/2 the universe would not be unstable to the formation of galaxies, and hence stars. On the other
|
|
hand, if go were much greater than 1/2, the age of the universe, which for such models is approximately
|
|
1/Hoqo^, would be so short that there would not have been time for stars to have been formed and to have
|
|
evolved. Hence we expect to find qo ~ 1/2.
|
|
|
|
An alternative explanation is that general relativity is
|
|
incomplete since it does not predict a unique cosmological
|
|
model. When we have found how to correct this defi-
|
|
ciency we will find that the only possible cosmological model is the Einstein-de Sitter model with qo = 1/2.
|
|
|
|
7
|
|
|
|
Either way the combination of go = 1/2 with the other large number relation gives the results:
|
|
|
|
e^po
|
|
|
|
Gnii
|
|
|
|
'
|
|
e^Ho
|
|
|
|
This line of argument has been pushed further by Carter [25] who argues that we need conditions which give some stars with convective outer envelopes since these stars have planets, but we cannot have completely mixed convective stars since supernovae require unmixed stars. This argument is quantified by requiring that the effective temperature of stars be approximately the ionization temperature of hydrogen {OAa^rUgc'^/k). This condition determines the mass of such stars as
|
|
|
|
The argument is now used that ac^'^a^*^ = 1 since if it were much greater all stars would be convective and mixed, whereas if it were much less then there would be
|
|
no stars with outer convective zones, and so no planets.
|
|
With ac — a^" we have ac ~ 10"^^ and the actual magni-
|
|
tude of the large numbers is 'explained'. Similar arguments to those above can be used to explain other numer-
|
|
ical constants of nature [26].
|
|
|
|
" 13. Critique of the Anthropic Program
|
|
|
|
My first objection to the anthropic program is that the
|
|
technical arguments have not been carried through; the
|
|
behavior of models with substantial different parameters
|
|
awaits evaluation. For example, could we not have a universe with qo = 10'^^? In such a model stars would
|
|
have evolved provided
|
|
|
|
1
|
|
|
|
!_ t
|
|
|
|
The arguments on galaxy and star formation are a little weak since we are still struggling to understand how gravitational condensations occur. The argument ad-
|
|
vanced by Carter to explain why ag ~ lO"*^ is very
|
|
weak. Firstly supernovae could occur in homogeneous evolution after evolution through to carbon stars, and secondly it is by no means obvious that convective zones
|
|
are a prerequisite for planetary formation. This criticism
|
|
however can and should be quantified by calculations on the properties of a universe with different values of the large numbers.
|
|
|
|
But if the program is successful, what does it tell us?
|
|
|
|
There are laws of nature (L, ) containing arbitrary con-
|
|
|
|
stants (a,) and a set of observations (Ot); and a subset of
|
|
|
|
these observations is the existence of ourselves. If the
|
|
|
|
theories are 'correct' then with the observed values of
|
|
|
|
the constants they must predict our existence. If they
|
|
|
|
did not predict our existence the theories would be
|
|
— wrong that is contradicted by observation. If we had
|
|
|
|
the same theories with different constants the predic-
|
|
|
|
tions would necessarily be different, and there is no rea-
|
|
|
|
son why those predictions should include the emergence
|
|
|
|
of mankind. The anthropic program is therefore bound to
|
|
|
|
We be successful.
|
|
|
|
exist in the universe and if we had a
|
|
|
|
full knowledge of the laws of physics, we would predict
|
|
|
|
our own existence.
|
|
|
|
The more fundamental problem is why there are any constants of nature at all, or indeed why there are any laws of nature. Is there a Creator who set up the
|
|
universe with just those initial conditions, laws, and constants of nature that would lead to the emergence of mankind? Is it just chance? Is there an infinity of 'parallel' universes with different laws and different constants,
|
|
|
|
each with its own properties? Our universe which con-
|
|
tains us then necessarily has those laws that give rise to mankind. Does the universe go through cycles in which the laws and constants of nature change? Could it be that there are really no laws or constants of nature, but
|
|
that we just live in a statistical fluctuation of order in a universe of chaos? Or are there unknown laws, con-
|
|
straints, consequences yet to be discovered that will ultimately lead us to the conclusion that there can only be one universe, one set of laws, one set of constants, one geometrical structure? Is there only one possible
|
|
universe with the properties we observe including our own existence?
|
|
|
|
14. Conclusions
|
|
|
|
I have tried to emphasize throughout this article that experiments are the final arbiter; in Poincare's words "Experiment is the sole source of truth" [27]. Yet mathematical physics has a vital role to play in developing ideas through to predictions that can then be compared to experimental data; and philosophy too has a role to play in challenging our firmly held views, in separating the meaningful from the meaningless questions.
|
|
|
|
I would therefore like to finish by encouraging the
|
|
|
|
reader to let his hair down occasionally and think of the
|
|
|
|
outlandish possibilities, which can in turn be developed
|
|
|
|
and tested. Is 'space' as determined by light signals lo-
|
|
|
|
cally Euclidean? Is gravitational time the same as inertial
|
|
|
|
time, spin time, electric time
|
|
|
|
Are the laws of phy-
|
|
|
|
sics 'here and now' the same as they were 'there and
|
|
|
|
then'? Is matter being created or destroyed? At what
|
|
|
|
level of accuracy will we find general relativity to be in-
|
|
|
|
correct? Does special relativity hold good as v
|
|
|
|
cl Do
|
|
|
|
the fine-structure constant and the particle mass ratios
|
|
|
|
vary in time at some level? The reader can add his own
|
|
|
|
ideas to such a list!
|
|
|
|
References
|
|
[1] Shu Ching, The Book of History (circa 2200 B.C.). For translations, see J. Legge, The Shoo King (The Author's Hongkong, London, 1865); C. Waltham, Shu Chiyig (Allen and Unwin, 1971). See also C. P. S. Menon, Early Astronomy and Cosmology (London, 1932).
|
|
[2] Chou Pi (circa 1100 B.C.). For a discussion of this model, see Thaibut, J. Asiatic Soc. of Bengal (1880); and C. P. S. Menon, Early Astronorny and Cosmology (London, 1932).
|
|
[3] Suryaprajnapti, Book 1, chapter 8 (circa 500 B.C.); see also W. Brennand, Hiridu Astronomy (London, 1896).
|
|
[4] D. Hume, An Inquiry Concerni7ig Human Understanding
|
|
(1748) [see also Open Court Edition, Chicago (1927)]. [5] Euclid, Elements (circa 300 B.C.); see also T. L. Heath, The
|
|
Thirteen Books of Euclid's Elements (Dover, New York,
|
|
1956).
|
|
[6] G. Leibniz (1674), published in Math. Schrifters, vol. 5, Ed. by C. I. Gerhardt (Ascher Schmidt, 1849), p. 88. See also
|
|
M. Kline, Mathematical Thought from. Ancient to Modem
|
|
Times (Oxford University Press, i972). [7] J. Machin, in W. Jones (Synopsis, London, 1706); see also K.
|
|
Kopp, Infinite Series (Hafner, New York, 1971), p. 253.
|
|
[8] H. Poincare, La Science et I'Hypothese (Villiers, Paris,
|
|
1902). [English transl.: G. B. Halsted (Dover, New York,
|
|
1952.]
|
|
[9] K. F. Gauss, Werke vol. 8 (B. G. Teubner, Leipzig, 1900), p.
|
|
177.
|
|
[10] K. F. Gauss, Werke, vol. 4 (B. G. Teubner, Leipzig, 1900),
|
|
p. 258.
|
|
['11] I. Newton, Philosphial Naturalis Principia Mathem/itica, London (1687).
|
|
|
|
8
|
|
|
|
[12] A. S. Eddington, Fundamental Theory (Cambridge University Press, 1946); E. A. Milne, Kinematic Relativity (Ox-
|
|
ford University Press, 1948).
|
|
[13] I. W. Roxburgh, in The Encyclopedia of Ignorance, Ed. by R. Duncan and M. Weston-Smith (Pergamon Press, Ox-
|
|
ford, 1977), p. 38.
|
|
[14] P. A. M. Dirac, Proc. R. Soc. London, Ser. A: 165, 199
|
|
(1938).
|
|
[15] H. Bondi and T. Gold, Mon. Not. R. Astron. Soc. 108, 372
|
|
(1948).
|
|
[16] E. A. Milne, Nature (London) 130, 508 (1932); and Relativity, Gravitation and World Stnicture (Oxford University Press, 1935).
|
|
[17] C. H. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961).
|
|
[18] S. Weinberg, Cosmology (Wiley, New York, 1972), p. 619.
|
|
[19] I. W. Roxburgh, Bicentennial Lectures on Cosmology,
|
|
University of Virginia, 1976 (unpublished).
|
|
|
|
[20] P. A. M. Dirac, Proc. R. Soc. London, Ser. A: 338, 439
|
|
(1974).
|
|
[21] I. W. Roxburgh, Nature (London) 268, 504 (1977). [22] V. M. Cannuto, P. J. Adams, S. H. Hsieh, and E. Tsiang,
|
|
Astrophys J. Suppl. Ser. 41, 243 (1979). [23] R. Ritter, these proceedings. [24] R. H. Dicke, Nature (London) 192, 440 (1961). [25] B. Carter, in Confrontation of Cosmological Theories and
|
|
Observation Data: Proceedings, Ed. by M. S. Longair (Kluwer Boston, 1974). [26] B. J. Carr and M. J. Rees, Nature (London) 278, 605 (1979).
|
|
[27] H. Poincare, La Science et I'Hypothese (Villiers, Paris, 1902). [English transl.: G. B. Halsted (Dover, New York,
|
|
1952), p. 140.]
|
|
|
|
9
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
FREQUENCY, WAVELENGTH, AND STORED IONS
|
|
|
|
Frequency Standards Based on Magnetic Hyperfine Structure Resonances
|
|
H. Hellwig
|
|
Frequency and Time Systems, Inc., 34 Tozer Road, Beverly, MA 01915
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Magnetic hyperfine resonances in alkali atoms were the physical basis of practical atomic frequency standards at the beginning of the age of the realization of the unit of time via atomic phenomena. This dates back more than 25 years; it appears to be no accident that today's time and frequency technology still rests on the same physical basis: practical frequency standards and clocks use magnetic hyperfine
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— transitions in cesium, rubidium, and hydrogen, and the unit of time is defined as well as practically — realized via the cesium resonance.
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This paper explores the basis for this phenomenon which is a result of a combination of mature electronics and physics technologies with proven principles of experimental physics such as beam spectroscopy and optical pumping. This paper will also address the limitations of these "traditional" or "microwave" frequency standards as well as opportunities still open for further improvements. These limitations and opportunities center around the desirability to achieve a spectrally narrow line; i.e., a high line-Q within the microwave region. Options to realize improved Q-values will be discussed.
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Key words: atomic clocks; cesium beam; frequency standards; hydrogen maser; rubidium gas cell.
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1. Introduction
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The resonances of cesium, rubidium, and hydrogen in the microwave region have dominated the atomic time and frequency standard field since the 1960's. In fact, rubidium and cesium standards now have been commercially available for two decades [1, 2]. The 1960's saw refinements in atomic clock design and their use in many scientific applications and in metrology including the generation of time on a world-wdde basis. The 1970' s can be characterized by the beginning of large-scale system-use of atomic time and frequency standards reaching far beyond scientific studies, making possible today's communication and navigation systems.
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An atomic time and frequency standard consists of
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three elements: the external interfaces, the electronic
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systems, and the atomic resonator. The atomic resonator is the heart of the atomic standard and serves the same function as the pendulum in a mechanical clock; however, with one most fundamental difference: The atomic resonance frequency itself is given by nature, it will not drift, nor will it age according to all of our present experimental and theoretical knowledge. Furthermore, all
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A atoms are the same. standard built independently from
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another standard will show the same characteristics and the same frequency as its predecessors or as standards in different locations. Atomic clocks feature an a priori accuracy; therefore, atomic clocks and frequency standards are often called primary standards.
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The frequency of the emitted or absorbed radiation is related to the energy difference between the two atomic energy levels. In the three alkali atoms, hydrogen, rubidium, and cesium, which are most prominently in use today, as they were for several decades, the magnetic hyperfine transition in the ground state (^Si/2) is being used. Table 1 shows a summary of these three standards and their characteristic frequencies. The transitions are between energy levels which are created by the spin-spin interaction between the atomic nucleus and the outer electron in the ground state of the atom. As such, the separation of the two energy levels, i.e., the transition frequency, is a function of the magnetic field. This
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dependency is described by the Breit-Rabi equation [3, 4] and depicted in Fig. 1.
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In order to define the precise resonance frequency, the external magnetic field has to be well defined and kept
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Table 1. Summary of rnost ividely used atoms.
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Atom
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Atomic Nuclear
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Mass
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Spin
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vr(Hz)
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Hydrogen (H)
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1
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Rubidium (Rb)
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87
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Cesium (Cs)
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133
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1/2
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1 420 405 752
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3/2
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6 834 682 608
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7/2
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9 192 631 770
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(F.mp)
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12
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0
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3
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X
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Figure 1. Energy level diagram of ^'^^Cs in the ^Sj!^ groiaid state as a function of the applied magnetic field.
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11
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constant. This necessitates magnetic shielding which is a characteristic design feature of all presently used atomic freqliency standards. The shielding can be quite elaborate, and reduces the external magnetic fields, foremost the earth's magnetic field, to one percent or less of its normal value. It is obvious that only the
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Amp = 0, the so-called clock transition, can provide
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highly stable reference frequencies. The transition proba-
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bility for this transition must be maximized and the
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corresponding probabilities for all other magnetic-field-
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dependent transitions must be minimized. This is done by
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applying a constant magnetic field, the so-called C-field.
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Amp In order to force the
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= 0 transition, the magnitude
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of the C-field is typically at least an order of magnitude above all anticipated residual field components, and its orientation is such that its vector is parallel to the vector
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of the oscillating field w^hich is coupled to the resonance of the atom. The resulting frequency shift can range up to parts in 10^ as compared to the frequency of the atom in a zero magnetic field.
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The magnitude of the field can be measured quite pre-
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cisely, actually to an accuracy which is much better than
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required in view of all other frequency stability limita-
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tions. Such a measurement is done by using the atom it-
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self as the magnetometer. In Fig. 2, which illustrates
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cesium for regions of relatively low magnetic field [4],
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the clock transition is indicated by the solid line. The
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H magnetic field
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can then be measured precisely by
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measuring the magnetic field dependent or Zeeman reso-
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nances at higher or lower frequencies as indicated by the
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We dotted lines between the energy' levels.
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note that we
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H can measure a magnetic field
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by measuring at mi-
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crowave frequencies or, alternately, by injecting a low
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frequency.
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—1
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^rr-
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-H
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1
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1
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H
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1
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1
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^
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t
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-Lt
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"
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rfJ i
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i_L_
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MAGNETIC FIELD
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"o ENERGY STATES AT H " Hn
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Figure 2. Magnetic field dependence of the hyperfine energy levels in the groundstate of the cesium- atom,.
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2. Design Principles of an Atomic Resonator
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Atomic frequency standards, fundamentally, are devices which allow the measurement of a microwave frequency with very high resolution and accuracy. The Doppler effect represents perhaps the most important problem limiting the accuracy and resolution of any frequency standard. In the usual way we can say that if an absorber of radiation moves relative to the source, the observed resonance frequency is shifted to the value [5]
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Wobs = Wo + K V - --
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2M?
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where the velocity v and wave- vector k are measured relative to the source. The first order Doppler shift (k • v), the second order Doppler shift (v/c)^/2, and the recoil shift (the last term) can be understood in terms of conservation of energy and momentum in the emission or absorp-
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tion process. Specifically, the so-called second order Doppler shift is merely the relativistic time dilation factor
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resulting from the movement of the atom relative to the
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apparatus. Its effect is small but ultimately important.
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The term "natural linevddth" normally refers to the emission of visible light where the natural linewidth
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describes the spectral linewidth associated with an optical transition. Lifetimes of optical transitions can be cal-
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culated from quantum mechanics using Planck's equation for the black-body radiator. The lifetime in a given state is proportional to the cube of the frequency; thus, at microwave frequencies we are faced with natural lifetimes of the states involved of hundreds of seconds. In other words, the natural linewidth is unmeasurably small in the microwave region as compared to other limitations. As a consequence, one may interpret for microwave frequency standards (Fig. 3), that the lifetime is given by the observation time allowed by the frequency
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standard apparatus or atomic resonator to coherently observe the atomic radiation. In general, this lifetime is limited by either of two general effects: (1) the atom enters and leaves the apparatus after a time At, or (2) the atom stops oscillating due to a collision with other
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atoms or the walls of the container after a time A t. Thus atomic frequency standards are characterized by maximizing At and, vdth it, the line-Q.
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A
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^ Doppler /
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Width
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\ Gaussian
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B
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Natural _^ Linewidth
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Lorentzian
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\^^^^^^aL|ss|an
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FREQUENCY
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FREQUENCY
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A Figure 3. Spectrum of an atomic transition. On the left, part
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shows the situation when the atoms are unbound and the reso-
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nance feature has the full Doppler width Av~ (vie) vq. When
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the atom is confined to dimensions less than the wavelength,
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the Doppler profile is suppressed and the central feature has the natural undth A v as shown in part B. (From Ref. [5].)
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Fundamentally related to this, again via Planck's equa-
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tion, is the fact that the population difference between the
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two levels separated by microwave frequencies is very
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« small. The population difference is a function of v. In the
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low gigahertz region where h v
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kT, the population
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difference is only a very small fraction of one percent.
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Therefore, in order to observe effectively the atomic reso-
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nance, it is a common design principle in microwave fre-
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quency standards to modify the population in the upper
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and lower state. Either one has to be significantly depopu-
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lated. The result is an atomic ensemble which either has a
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significant net emission or net absorption of energy. The
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way in which this is accomplished is a significant deter-
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minant in the design of an atomic resonator.
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In summary, the design of an atomic resonator is
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characterized by the particular method of maximizing the
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coherent observation time, minimizing first order Doppler
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effects, and achieving a significant net population differ-
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ence between the two microwave energy levels.
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12
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.
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)
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3. Performance Principles
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Time and frequency standards can be characterized in numerous ways. However, most frequently, a time domain characterization is most lucid and useful. The quantity measured [6] is the two sample or Allan vari-
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ance (Tyir) defined as
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where y is the fractional frequency of adjacent measurements each with a sample time t, and the brackets denote
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an infinite time average.
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An idealized presentation [1] for all precise time and
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frequency standards is shown in Fig. 4. The first part, I,
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of the stability plot is determined by the fundamental
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noise processes present in the standard and can be
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characterized by the equation a,/T) = /cit ^ The second
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part, II, is called the flicker or frequency floor, which
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describes an independence of o-,/(t) from the averaging
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We time.
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shall call this value dyp. Its level depends on
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the particular frequency standard and is not fully under-
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stood in its physical basis, but relates to fluctuations in
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the value of critical, frequency-determining parameters
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of the standard. The last section. III, can again be
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characterized by a,y(T) ^ k-zT ~. The coefficients ko and
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cannot usually be determined very accurately because of
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the long measurement times needed in order to obtain
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statistical confidence. These coefficients are subject
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largely to environmental effects and are thus not stable.
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If linear frequency drift is present, az - +1. Of course,
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drift is always caused by some systematic change in a
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frequency determining parameter with time. In contrast.
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Regions I and II have more quantifiable physical rela-
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tionships. The approximate relationship between fre-
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quency stability in Region I and the signal to noise avail-
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able in the device can be given by (JyiT) — (Q S/N)"\
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S/N is the signal to noise ratio which, of course, is a
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function of the sampling time t. The quality factor of the
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resonance line enters as a key determining factor: the
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larger the Q, the better the stability. However, Q and
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S/N can be traded against one another.
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A device with a relatively low Q and a large S/N gives
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the same short-term stability performance as a device
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with a high Q and a low S/N. S/N can be expressed in
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terms of physical parameters of the atomic resonators
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which typically are shot-noise-limited: If n is the number of signal events per unit time, S/N = VnV.
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II III.
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WHITE OR FLICKER OF PHASE NOISE WHITE FREQUENCY NOISE FLICKER "FLOOR" (FLICKER OF FREQUENCY
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1 PURE FREQUENCY DRIFT (AGING)
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Figure 4. Typical frequency stability behavior of a frequency standard. The two-sample variance is ^ (j).
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The flicker floor. Region II in Fig. 4 (cTyf), appears to be related to the Q-value of the resonance. Qualitatively, this is not surprising. Atomic resonators with Q-values of 10* or higher may be expected to have accuracies of one part in 10* or better because the linewidth is acting like an ultimate limit on the variability of the frequency of
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the resonance [7]. We can summarize: A high resonator Q
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is essential to achieve high accuracy and ultimate stability. Thus, the time keeping potential of an atomic clock is governed by the Q-value and not by the signal-to-noise. Signal-to-noise is only important to assure sufficient short-term frequency stability so that measurement periods of acceptably short duration are needed to realize the available accuracy.
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4. Electronic Systems
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Figure 5 depicts the general concept of the overall design of an atomic standard where the atomic resonator serves as the frequency reference for a slave oscillator (usually a quartz crystal) in a servo loop configuration.
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Figure 5. Block diagram of an atomic clock mth a frequency
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lock servo.
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Frequency-lock servos are used in passive atomic
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clocks (e.g., cesium beam and rubidium gas cell) to steer
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the frequency of the reference oscillator so that it coincides with that of the atomic transition. The atomic resonator behaves similarly to a simple band-pass filter followed by a square-law detector. Therefore, in the fol-
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lowing, we will assume that the "line shape" of the
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detected signal S (co) versus applied rf frequency is
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Lorentzian, i.e.,
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S(co) = So (1 + (v - vo)2/Avf )-\
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where vq is the atomic frequency, Av; is the line width,
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and V is the frequency of the source (multiplied reference
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oscillator). S (w) is plotted in Fig. 6. Although some de-
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vices do not exhibit such line shapes, the qualitative
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We results discussed below still apply.
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can use the S (co)
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curve as a frequency discriminator; one common way is
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to use sinewave frequency modulation (FM) on the
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source. In this case v —
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+ A v», sin aj,„ t where A
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is
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FM the
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swing and co,,, = 2Tr v,,, the modulation frequency.
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If we now mix this signal with a reference signal pro-
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portional to sin 0),,, t, as shown in Fig. 5, then the output of the mixer has output near dc (i.e., neglecting 2w,„
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terms) of
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V. - -F
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Av„i(vs - Vo)
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+D ,
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(Av,)2 1 +
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A V;
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where F depends on the input levels to the mixer and
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mixer efficiency and Z) is a possible mixer output offset.
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Figure 6. Plot of atomic resonance features assuming a
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Lorentzian line shape. S (w) is detected signal versus fre-
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quency. Vq(w) is the detected signal compoyieyit (at frequency
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« v„, ) wheyi the amplitude of the frequency modulation is small
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(Av,„
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Av;).
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This output voltage as a function of frequency is plotted
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in Fig. 6 and can be used to servo the frequency of the os-
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cillator (VCO) as shown in Fig. 5. For good long-term sta-
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^ bility and accuracy, we want the gain G (co = 0)
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ao;
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therefore this part of the servo is usually an integrator.
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Depending on the particular design of the servo electron-
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ics, frequency offsets, frequency instabilities, and fre-
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quency drifts can be induced which usually relate to phase
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and gain changes. However, proper design and alignment
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can nearly arbitrarily reduce such phenomena.
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It is possible to operate an atomic standard as an ac-
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tive oscillator or maser oscillator. It is necessary,
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nevertheless, to include frequency synthesis and elec-
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tronic servo principles in such a device because the out-
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put signal is not a standard frequency and, typically, has
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a very low power level (order of picowatts).
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The electronic system of a maser oscillator frequency
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standard is depicted in Fig. 7. The output of the maser
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is amplified in a wideband amplifier, and then fed into a
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double heterodyne receiver which ultimately translates
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the frequency down to dc. This dc voltage is used to con-
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trol the frequency of the crystal oscillator which drives
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the double heterodyne system. In other words, the crys-
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tal oscillator is phase-locked to the maser frequency.
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Such frequency standards are called "active" devices (in
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contrast to the "passive" principles discussed above).
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In both "passive" as well as "active" systems, the slave oscillator is of special importance because its performance determines, in part, the frequency stability of the whole standard. For averaging times of less than those corresponding to the unity gain of the servo loop, the frequency stability is essentially that of the slave oscillator; for times larger than that, the atomic resonator dominates the stability performance. It must be noted here that an inferior slave oscillator, i.e., an oscillator with a frequency stability worse than that of the atomic resonator at the unity gain point, will correspondingly reduce the frequency stability of the system for some range of averaging times. Thus, in the design of a complete frequency standard, the choice of both the stability characteristics of the slave oscillator as well as the atomic resonator in combination with the selection of the time constant of the servo loop or bandwidth which determines the unity gain point, is critical to achieve op-
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timum overall system performance.
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5. The Cesium Beam Standard
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The cesium standard was the first and still is the most important of all atomic standards. Developed in the early
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1950' s, its first operational use as a laboratory clock
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came about in 1955 at the National Physical Laboratory in the United Kingdom, and its first commercial realization took place in 1958 at the National Company in Massachusetts, U.S.A. Today, a variety of laboratory-type and commercial standards exist [1], and the world's internationally coordinated time system is based on a large number of cesium standards of worldwide distribution. The laboratory devices, or primary standards, are used to define the unit of time, the second [8]. This is done by constructing the apparatus in such a way that most known perturbing parameters can be independently and separately measured. Then, corrections can be applied to the output frequency in order to realize, as best as possible, the unperturbed resonance frequency of the cesium atom at rest in free space [9, 10, 11].
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Figure 8 depicts the schematic design of a cesium beam standard omitting the electronic systems. The oven is constructed in such a way that an ampule containing
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cesium can be inserted and opened inside of the oven via
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a remote mechanism after the beam device has been
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evacuated to very low pressures. Pressures of better
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than 10^^ Torr are needed to allow sufficient mean free path from source to detector. Oven temperatures used vary between 60 and 120 °C, providing vapor pressures
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MAGNETIC SHIELD
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OUTPUT FREQUENCr
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|SYNTHESIZE«]
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A
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1^^>—- [~HI X
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VARACTOB TUNABLE
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X-TAL OSCILLATOR
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Figure 7. Schematic of a maser oscillator frequency standard.
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Figure 8. Schematic of a cesium atomic-beam resonator. The frequency input is derived from a quartz-crystal oscillator (typi-
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cally at 5 MHz) with a frequency multiplier and synthesizer to
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generate the atomic resonance frequency . A feedback servo from
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the detector output then controls this oscillator.
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14
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in the range from 10"'' to 10"^ Torr inside of the oven.
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The state selectors for a cesium beam are typically dipole
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magnets, but multiple dipole, double-dipoles, and hexapole magnets have been used. Dual-beam devices have
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been built which utilize simultaneously the upper and lower state by generating two different beams deflected in opposing directions [10].
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Vacuum is typically maintained by ion pumps; these feature rather sizeable pump capacities in the case of
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laboratory-type standards, but are as small as 0.1 l/s
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internal pumps in the case of commercial cesium standards. These small pumps serve only to scavenge residual gases, most importantly noble gases. Since prior to permanent seal-off a commercial tube is baked at high tem-
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peratures, there is very little evolution of gases inside of the tube; furthermore the expended cesium acts as an ef-
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fective getter for many gases. The waste-cesium itself is
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gettered by strategically placed graphite in solid, as well
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as in surface deposition form.
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The detector in cesium standards is typically a hot wire. The low ionization potential of the cesium atom makes it possible to surface-ionize cesium atoms on me-
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,
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tals with a sufficiently large work function. Metals which are being used include tungsten, niobium, and tantalum, as well as platinum-iridium alloys. Since most of these metals contain significant amounts of contaminants, in particular, potassium, the ions formed on the surface of the hot wire are extracted through a mass spectrometer. The mass spectrometer is typically a magnetic field, bending the ions by 90 degrees out of the original path of the incoming neutral atoms. The ions are collected on an electrode. In some high intensity beam laboratory devices the current is directly detected by an electronic
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amplifier [9, 10, 11], typically with a field-effect transistor front end. In all commercial devices, however, a tube-internal electron multiplier is used. Thus, the collector electrode becomes the first dynode of the multiplier. The electron multiplier provides sufficient gain to raise the signal level by orders of magnitude above the noise level of electronic amplifiers. The surface ionization efficiency, together with the low noise of an electron multiplier, allows an essentially noise-free detection of
|
|
single atoms in cesium beam devices.
|
|
The speed of the atoms and the length of the interac-
|
|
tion region determine the Q of the cesium resonator.
|
|
Atomic velocities at the most probable thermal velocity
|
|
are 200 to 250 m/s. In many practical cesium beam tubes, a lower velocity is selected by the beam optics, typically close to 100 m/s. Thus we find Q values ranging from a
|
|
few 10^ to a few 10^ over the spectrum of commercial and laboratory devices. Typical beam intensities at the detector are of the order of 10'' to 10^ atoms per second corresponding to electronic currents of the order of picoamperes. The resulting signal-to-noise for averaging times of one second is several thousand and allows fractional frequency stabilities at one second in the range from 10"^" to 10"^*^. Cesium is preferred over other atoms because of its convenient frequency, permitting the use of readily available electronic techniques while featuring a sufficiently high resonance frequency for achieving high
|
|
Q values; cesium has sufficient vapor pressure not far above room temperature, and the detectability of cesium by surface ionization is nearly 100% efficient.
|
|
The most significant limitation to frequency stability and accuracy of cesium beam devices appears to be the distributed cavity phase shift [12, 13]. It arises from the fact that the cavity phase is distributed along the axis as well as across both coordinates of the plane perpendicu-
|
|
|
|
lar to the beam. As a result, different trajectories sample
|
|
|
|
different cavity phases in each of the two interrogation
|
|
|
|
regions; and the cavity phase difference which affects the
|
|
shift of the Ramsey pattern becomes trajectory depend-
|
|
|
|
ent. Since with spatial state selection the trajectories
|
|
are velocity dependent, we have a two-parameter depend-
|
|
|
|
ence of the effective cavity phase shift, and thus of the
|
|
|
|
apparent resonance frequency. Since the distributed cav-
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|
|
|
ity
|
|
|
|
phase
|
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|
|
shift
|
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|
|
can
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|
be
|
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|
|
assumed
|
|
|
|
to
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|
|
be
|
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|
of
|
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|
the
|
|
|
|
order
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|
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|
of
|
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|
""^
|
|
10
|
|
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|
to 10"^ radian, cesium tubes suffer from this effect,
|
|
|
|
depending on their resonance line Q, anywhere between
|
|
|
|
10"^"^ to 10"". Since optimum power is a function of the
|
|
|
|
velocity, we have a change of the average trajectory lo-
|
|
|
|
cation with microwave power, and thus frequency shifts
|
|
|
|
as a function of microwave power. Other related shifts
|
|
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|
[13] include temperature gradient related frequency
|
|
|
|
shifts, acceleration or gravitationally induced frequency
|
|
|
|
shifts, vibration induced perturbations, and voltage re-
|
|
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|
lated frequency shifts, e.g., those caused by change in the
|
|
|
|
collector voltage potential near the hot wire [14] (causing
|
|
|
|
a samphng of different regions of the hot wire
|
|
|
|
corresponding to different atomic trajectories). Thus,
|
|
|
|
state selection and detection techniques which are uni-
|
|
|
|
form across the beam and retain spatial isotropy of the
|
|
|
|
velocity distribution would essentially remove all effects
|
|
|
|
related to the distributed cavity phase shift. Optical
|
|
|
|
pumping appears to be an elegant means to this end, but
|
|
|
|
at this point in time insufficient experimental data are
|
|
|
|
available to support its practical feasibility. Optical
|
|
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|
detection would be a combined function of the second
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|
state selector which, if optically executed, would interro-
|
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|
|
gate the population levels and act as a photon
|
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|
transformer for the detection of microwave-induced
|
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|
atomic transitions.
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|
|
6. The Rubidium Gas Cell Standard
|
|
The traditional design of a rubidium standard features a lamp filled with rubidium 87 isotope, a filter with rubidium 85 isotope, and the cell featuring again rubidium 87 isotope [15]. As illustrated in Fig. 9, it is a happy coincidence that the optical absorption lines of rubidium
|
|
85 largely overlap with one of the hyperfine splitting components of the rubidium 87 pumping light; thus the insertion of the rubidium 85 filter effectively suppresses the light which otherwise would couple to the upper microwave level of rubidium 87. This results in efficient optical pumping, i.e., in population of the upper
|
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|
-6.835 GHz
|
|
|
|
ENERGY = hi/
|
|
Figure 9. The solid curves represent optical emission correspondim to the desired (F = 1) ayid the undesired (F = 2) states of Rb. The dashed curves represent absorptions corresponding to the filter action of^^Rb.
|
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15
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|
.
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|
microwave level, while the lower level essentially is fully depopulated.
|
|
Figure 10 shows the schematic of a rubidium gas cell frequency standard. In order to achieve full efficiency of the system, the vapor pressure in the gas cell has to be adequately high; partial pressures of 10"^ to 10"^ Torr are a reasonable compromise between achieving good signals while avoiding significant numbers of spin exchange collisions between rubidium atoms which would lead to frequency shifts [16] and also shorten the relaxation time and thus the line Q. In order to obtain the needed light intensity, the rubidium pressure in the lamp has to be at a higher level, and, typically, temperatures between 120 °C and 180 °C in the lamp are used. The filter temperature is adjusted to a temperature between those of the lamp and the gas cell. The gas cell features a buffer gas mixture typically containing two components, one with a positive pressure shift on the rubidium frequency, the other with a negative shift, compensating each other's temperature coefficients [17]. In practice the residual temperature coefficient is not much less than 1
|
|
part in
|
|
MAGNETIC SHIELD
|
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|
|
Rb LAMP
|
|
JL
|
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|
|
Rb-85 BUFFER GAS
|
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|
|
Rb-87 t BUFFER
|
|
GAS
|
|
|
|
r.f LAMP EXCITER
|
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|
|
POWER SUPPLIES FOR LAMP, FILTER
|
|
AND ABSORPTION CELL THERMOSTATS
|
|
|
|
Figure 10. Schematic of a ruhiduyn gas cell frequency standard.
|
|
Usually, the rubidium is in a liquid/gas equilibrium, provided via a relatively cooler appendix in the rubidium gas cell. The appendix is cooled via thermoelectric cooling or by providing a thermal gradient oven with higher temperatures for most of the gas cell with the exception of the appendix. Alkali-resistant glass must be used to minimize reaction as well as absorption
|
|
and diffusion of rubidium into the glass. Some diffusion
|
|
of rubidium into the glass always exists; thus, overfilling with rubidium is typically the procedure in manufacturing the lamp, filter, as well as the gas cell. Rubidium depletion into the glass is responsible for the fact that the rubidium vapor pressure is not in true equilibrium with the liquid phase as would be calculated from the temperature of the appendix containing the liquid phase. The lamp is typically excited by an rf-discharge in the hundred megahertz range. The rubidium gas cell is housed in a cavity with low Q. The microwave signal can be generated externally or by harmonic generation internal to
|
|
A the cavity using a varactor diode. separate filter cell is
|
|
not absolutely necessary. If the rubidium gas cell is filled with an isotopic mixture of rubidium 85 and rubidium 87, the light of the lamp penetrating the first layers of this isotopic mixture will shift in its spectral charac-
|
|
teristics in such a way as to effectively pump the
|
|
remainder of the gas cell. In other words, this "integrated" gas cell [18] acts hke a filter cell at the side facing the lamp and, on the opposite side, like the gas cell resonator. The detector is typically a photocell, i.e..
|
|
|
|
a photo-voltaic device, which has a surface area commensurate with the effectively used light beam (of the order of 1 centimeter diameter). Unlike the case of the cesium standard, there is no optimum power. The reason for this is the fact that we have no transit-time phenomena as in a cesium beam, but rather the relaxation spectrum of the rubidium atoms due to collisions or radiation phenomena. Best conditions are obtained by selecting the microwave power in such a way that the product of signal-to-noise
|
|
and line Q is optimized.
|
|
As discussed above, the atomic ensemble does not perform spatial averaging but rather acts as a superposition
|
|
of the individual resonance frequencies of the spatially fixed atoms leading to an inhomogeneous resonance line.
|
|
As a result, dependencies occur against all parameters which are spatially selective [19]. This includes light intensity, magnetic field gradients across the cell, and microwave power due to the mode structure of the microwave cavity. In summary, the rubidium gas cell standard is a less "primary" device than the cesium beam tube. Basic frequency shifts due to buffer gas and light are of the order of parts in 10^ to parts in 10^. The rubidium
|
|
standard thus is sensitive to the stability in time of those parameters which cause these shifts [20]. Therefore, it is no surprise that rubidium gas cell standards show systematic frequency changes on the order of 10"^^ to 10"^^/day, corresponding to parameter changes as a function of time on the order of 10"^ to 10^^/day.
|
|
One of the primary limitations of the rubidium gas cell standard is the fact that it features an inhomogeneous
|
|
line. In order to transfer the rubidium gas cell into a standard with a homogeneous line, the buffer gas has to be essentially removed in order to realize effective spatial averaging of the individual atoms. As a result, wall collisions dominate as was shown experimentally [21] using high-polymer coatings such as paraffin and polyetheylene as wall materials. This approach allows the removal of the buffer gas while retaining the optical pumping principle with separate filter or isotope mixture in the gas cell. Unresolved at this time is the stability in
|
|
time of the coating materials when exposed to rubidium.
|
|
Another limitation of rubidium standards appears to be the residual light shift. One portion of the light shift is due to the inhomogeneous line and would be cured with the wall coating approach and spatial averaging. The other remaining light shift is due to the insufficient overlap of the rubidium 85 absorption and the rubidium 87 emission (see Fig. 9). This leads to an asymmetric spectral filtering of the rubidium 87 line which pumps the lower microwave" level. This light shift could be removed if a light source is employed which is centered and symmetrically coupled to the upper microwave level. Obviously, this can only be a laser source. The limitation of a practical standard would then be the stability of the laser frequency with temperature.
|
|
7. The Hydrogen Maser
|
|
An atomic hydrogen maser is depicted schematically in
|
|
Fig. 11. It is shown in operation as an active maser oscillator. The beam source is a glass container in which atomic hydrogen is created in a radio-frequency discharge from molecular hydrogen. Molecular hydrogen is supplied from a hydrogen source, such as a bottle, or in some more recent experiments, from metal-hydrides at elevated temperatures. The hydrogen beam is formed by a collimator which can be a single channel or a multichannel design. The hydrogen beam intensity is determined by the power of the dissociating discharge, as well as the
|
|
|
|
16
|
|
|
|
"C-FIELO"VACUUM ENVELOPE -
|
|
|
|
MAGNETIC SHIELD
|
|
|
|
KASER FREQUENCY
|
|
OUTPUT 1.4?0.405,7S1 Hz
|
|
|
|
. OlSSOCIATOB/BEAH SOURCE
|
|
|
|
VALVE POWER SUPPLY
|
|
Figure 11. Schernatic of an atomic hydrogen maser frequency
|
|
standard.
|
|
flux of molecular hydrogen. In order to achieve stable
|
|
beam intensities, it is mandatory to regulate both the power of the dissociating discharge as well as the supply
|
|
of molecular hydrogen. Palladium metal has the property that, at elevated temperature, it has a very high diffusion coefficient for molecular hydrogen, while essentially remaining impermeable to all other gases. Thus via temperature changes it can operate as a regulated leak while at the same time purifying and rejecting impurities in the hydrogen gas. For effective dissociation, the typical
|
|
pressure in the source which operates at around 100 MHz
|
|
is 10"^ Torr.
|
|
The beam, W'hich is formed at the output of the source, must be state selected [22]. The state selector almost always is a multipole, axially symmetric magnet, which achieves high field strengths while providing an axially symmetric state selected beam as well as some limited spatial focusing. The most probable velocity is focused on the entrance aperture of the storage bulb. The storage bulb is placed inside of a TEOll cavity. In order to retain a high cavity-Q, the storage bulb is typically made out of quartz which shows very low dielectric losses. The inside of the storage bulb is coated with a high-polymer substance. Fluorocarbons such as Teflon have provided the
|
|
best surfaces, allowing highly elastic colhsions. Typi-
|
|
cally, many thousands of collisions can take place before
|
|
sufficient phase error is accumulated to de-correlate the radiation process. If the cavity-Q is high enough, i.e., cavity losses are low and the supply of state selected hydrogen is sufficiently high, the energy transferred into the cavity by the state selected hydrogen atoms exceeds the energy losses of the cavity and its associated electronics: the maser becomes an oscillator, providing a frequency close to the atomic resonance frequency of atomic hydrogen at 1,420,405,752 Hz. It is desirable to achieve
|
|
oscillations at the lowest possible beam intensities to make the storage time in the storage bulb as long as pos-
|
|
sible. Since storage times in excess of one second are possible, the escape relaxation time of the bulb, i.e., the flow of gas in or out of the bulb, is arranged in such a
|
|
way as to be just below the wall collision relaxation time of the hydrogen atoms for optimum performance. Storage
|
|
times of about one second lead to line-Q values of above
|
|
10^. These are the highest Q values in all presently used
|
|
atomic standards, and are the basic reason for the exceptional performance of the atomic hydrogen maser. The output of the device is a signal at the picowatt level.
|
|
For an active maser oscillator, the crystal oscillator is still needed in order to provide a standard frequency
|
|
A output. signal which is derived from the crystal oscilla-
|
|
|
|
tor is generated at the atomic hydrogen maser frequency. This signal is compared to the output of the atomic hydrogen maser using a superheterodyne, multistage receiver, as was discussed in section 4. Ultimately, the output of a phase detector is used to servo the crystal oscillator to be phase-coherent with the atomic hydrogen maser output signal. For this type of servo, which is phase sensitive, the frequency stability improves as the inverse of the averaging time t, as compared to a t"^ dependency for frequency-lock servos such as those in the "passive" cesium beam and rubidium gas cell standards. In an active device, cavity pulling is more pronounced [23]. Cavity pulling can be approximated by the
|
|
following equation:
|
|
|
|
-— V - VR -
|
|
|
|
- (Vc
|
|
|
|
Vr) .
|
|
|
|
We note that the pulling factor translating the cavity
|
|
offset into the frequency offset of the standard is the simple ratio of the cavity-Q and the line-Q as contrasted to the square of this ratio for passively operating devices (far below oscillating threshold). The puUing factor in typical hydrogen masers is of the order of 10"^ for the translation of cavity frequency offsets into output frequency offsets. Thus, active hydrogen masers are characterized by designs to stabilize the microwave cavity. This stabilization can be done by using low thermal expansion materials such as pure quartz as the cavity material
|
|
within an oven enclosure. Such ovens may yield tempera-
|
|
ture stabilities of better than one millidegree.
|
|
There is an alternate way to stabilize the microwave cavity's resonant frequency [22]. By increasing the amount of hydrogen supplied to the storage bulb, an increasing number of spin-exchange collisions between the
|
|
hydrogen atoms take place, shortening the radiation lifetime of the hydrogen atoms. The result is a broadening of the resonance line, i.e., a decrease in the line-Q. If the cavity is not tuned perfectly, the pulling equation leads
|
|
to a frequency change as a result of the change in Q due
|
|
to spin-exchange. Thus, a modulation of the hydrogen
|
|
beam intensity results in a modulation of Q which can be used to determine the point where (v - vr) becomes zero
|
|
and the cavity is properly tuned.
|
|
For hydrogen beam intensities insufficient to provide self-sustained oscillations, microwave radiation, i.e., its amplification, can be detected by using a microwave re-
|
|
ceiver, and a crystal oscillator can be servoed to the atomic resonance signal [24]. In this process, frequency or phase modulation in conjunction with either the absorption feature or the dispersion feature of the atomic resonance can be used to generate the reference signal for locking the crystal oscillator. This is the principle of the passive atomic hydrogen maser [25]. Since the detection of the atomic resonance still relies on the (phasesensitive) measurement of the atomic radiation, the pulling equation for the active maser still applies. Therefore, cavity stabilization is as important for a passive maser as for the active one with the only difference that
|
|
lower cavity-Q values may be used. An elegant method
|
|
for cavity stabilization is the absolute probing of the cavity resonance by injecting sidebands into the \vings of the cavity resonance and detecting any mistuning of the cav-
|
|
ity. This is shown in Fig. 12 where two servos are employed [25], one at a high frequency such as 10 kHz to probe the cavity resonance and a much slower modula-
|
|
tion, e.g., at 1 Hz, locking the crystal oscillator to the atomic reference frequency.
|
|
It must be noted that one of the exquisite features of the atomic hydrogen maser in the active mode is that its
|
|
|
|
17
|
|
|
|
1420 MHi CAVITY
|
|
Figure 12. Block diagram of a passive hydrogen maser frequency standard.
|
|
stability improves as t"^ Stabilities of 10"^^ at 1000 seconds have been achieved and stabilities in the 10"^^ range
|
|
have been repeatedly reported. We are rejninded that
|
|
the main reason for this superb performance of the hydrogen maser is the line-Q which exceeds that of the longest cesium beam tube by almost an order of magni-
|
|
tude. We remember that the concept of optimum power,
|
|
so convenient in the case of the cesium atomic resonator, is absent in the case of the hydrogen storage principle, as
|
|
it was in the case of the rubidium gas cell. Again, we have an exponential relaxation phenomenon in the
|
|
storage bulb, which is due to the escape of atomic hydrogen out of the storage bulb. Thus, increasing microwave power leads to interrogation of atoms with lesser relaxa-
|
|
tion times and corresponding line broadening, much as in
|
|
the case of the rubidium gas cell. Again, in the passive hydrogen maser, the microwave power is set in such a
|
|
way as to maximize the product of line-Q and signal-to-
|
|
noise.
|
|
It is difficult to imagine a storage-type device with a performance exceeding that of the hydrogen maser. This is based on the fact that the hydrogen atom is the small-
|
|
est of all atoms and permits a maximum number of collisions with minimum relaxation.
|
|
As we discussed many times, the very high line-Q of
|
|
the hydrogen storage principle leads to a very low flicker or frequency floor, as well as to excellent long term time-keeping performance. The key to frequency fluctuations in medium and long term is cavity pulling. The elimination of cavity pulling appears most elegant with the passive maser principle. The passive principle also allows less costly, more practical and smaller devices [26, 27, 28, 29]; however, the reduced cavity volume (e.g., of a dielectric cavity) leads to less available volume for the storage container, and thus increased wall-relaxation and consequential reduction in the line-Q. Unfortunately, for the purpose of this discussion, it appears that the reduced sensitivity to cavity pulling due to the lower cavity-Q and the passive control principle is compensated by the lower line-Q which leads to increased susceptibility to
|
|
frequency perturbing parameter changes. Thus, it may
|
|
be concluded that for excellence in clock performance (i.e., a very high line-Q), a so-called full-size passive hydrogen maser appears to be the most promising device
|
|
realization.
|
|
|
|
8. Fundamental Advances
|
|
|
|
As compared to today's microwave frequency stand-
|
|
ards, fundamental improvements in both Q and signal-
|
|
to-noise appear to be possible only by the use of higher frequencies, including infrared and optical frequencies. If it is assumed that these higher frequencies do not pose additional technical problems, the advantages are obvi-
|
|
ous: For the same length of the device, the Q improves
|
|
with the resonance frequency. Thus a device with a reso-
|
|
nance at 100 GHz and otherwise similar dimensions, has a 10 times improved Q as compared to cesium, and in the
|
|
near infrared and visible regions, an enhancement by a factor of 10,000 is available. With such enhancement fac-
|
|
tors, Q could be traded against signal-to-noise, by build-
|
|
ing smaller devices making more efficient use of the spatial acceptance limitations, or by multiple interrogation of the atoms or molecules, cycling each atom several times through its two states. Another technically elegant solution is optical pumping for state selection and possibly also detection. Optical pumping was tried on the rubidium beam and, more recently, on the cesium beam, originally with rf-excited lamps, but more recently with lasers, including diode lasers and dye-lasers. The principle advantage of this technique is that it removes the dis-
|
|
tributed cavity phase shift limitation.
|
|
|
|
Apparently, ion storage is the only known technique offering line-Q' s well in excess of 10^*^ in the microwave region. Although ions with resonance frequencies in the
|
|
infrared or visible radiation region are typically considered, very attractive resonances can be found in the
|
|
GHz region. Most importantly this includes mercury with hyperfine resonances at about 26 and 40 GHz
|
|
[30,31,32,33]. The achievement of very high line-Q's
|
|
is a result of stable storage in electromagnetic fields [34].
|
|
The most attractive and elegant solution is the radio-
|
|
frequency ion trap. An analysis of the frequency shifts
|
|
due to this confinement method has shown their influence to be less than 10"^^ The main drawback of this method is the difficulty in determining the speed of the ions which is needed to calculate the second order Doppler
|
|
|
|
effect.
|
|
|
|
Both the first and second order Doppler shifts could be
|
|
|
|
reduced in a fundamental way if the atoms could be
|
|
|
|
slowed down or cooled. Ion traps offer the possibility of
|
|
|
|
using radiation pressure to cool. Recently tunable,
|
|
|
|
narrow-band optical sources have become available which
|
|
|
|
make detection of the small number of ions much easier
|
|
|
|
than in the past and effective cooling possible. Typically,
|
|
|
|
not many more than 10"* ions can be stored and cooling of
|
|
|
|
electromagnetically confined atoms or ions has been
|
|
|
|
demonstrated [35, 36]. Optical pumping appears to be
|
|
|
|
necessary to effectively interrogate any stored ion-
|
|
|
|
ensemble without perturbation. Other auxiliary tech-
|
|
|
|
niques in need of refinement for practical uses include
|
|
|
|
the generation of ions and the interrogation by a micro-
|
|
|
|
wave signal.
|
|
|
|
J
|
|
|
|
References
|
|
[1] H. Hellwig, Proc. IEEE 63, 212 (1975). [2] N. F. Ramsey, IEEE Trans. Instrum. Meas. IM-21, 90
|
|
(1972).
|
|
[3] N. F. Ramsey, Molecular Beams (Oxford University Press,
|
|
London, 1956). [4] R. C. Mockler, Adv. Electron Electron Phys. 15, 1 (1961). [5] H. Hellwig, K. M. Evenson, and D. J. Wineland, Phys. To-
|
|
day, December, p. 23 (1978).
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|
|
|
18
|
|
|
|
[6] J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B.
|
|
Leeson, T. E. McGunigal, J. A. Mullen, Jr., W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler,
|
|
IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
|
|
[7] H. Hellwig, Radio Sci. 14, 561 (1979).
|
|
[8] M. Granveaud and J. Azoubib, IEEE Trans. Instrum. Meas.
|
|
IM-25, 469 (1976).
|
|
[9] G. Becker, Metrologia 13, 99 (1977).
|
|
[10] D. J. Wineland, D. W. Allan, D. J. Glaze, H. W. Hellwig,
|
|
and S. Jarvis, Jr., IEEE Trans. Instrum. Meas. IM-25,
|
|
453 (1976). [11] A. G. Mungall, H. Daams, D. Morris, and C. C. Costain,
|
|
Metrologia 12, 129 (1976). [12] L. L. Lewis, D. A. Howe, S. R. Stein, C. Manney, M.
|
|
Mohler, J. C. Berquist, D. J. Wineland, and F. L. Walls,
|
|
CPEM Digest 1980 (IEEE Catalog No. 80CH1497-7 IM,
|
|
1980), p. 129.
|
|
[13] D. J. Wineland, Metrologia 13, 121 (1977).
|
|
[14] D. W. Allan, H. Hellwig, S. Jarvis, Jr., D. A. Howe, and R. M. Garvey, Proc. 31st Annual Symp. on Freq. Control
|
|
(Electronics Ind. Assoc., Wash., D.C., 1977), p. 555.
|
|
[15] P. Davidovits and R. Novick, Proc. IEEE 54, 155 (1966). [16] M. Tetu, R. Fortin, and J. Y. Savard, IEEE Trans. In-
|
|
strum. Meas. IM-25, 477 (1976).
|
|
[17] G. Missout and J. Vanier, IEEE Trans. Instrum. Meas. IM-
|
|
24, 180 (1975).
|
|
[18] E. Jechart, Proc. 27th Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C. 1973), p. 387.
|
|
[19] A. S. Risley and G. Busca, Proc. 32nd Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C,
|
|
1978), p. 506.
|
|
[20] P. Cerez and F. Hartmann, IEEE J. Quantum Electron.
|
|
QE-13, 344 (1977).
|
|
[21] G. Busca, R. Brousseau, and J. Vanier, IEEE Trans. In-
|
|
strum. Meas. IM-24, 291 (1975).
|
|
|
|
[22] D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, Phys. Rev. 138, A972 (1965).
|
|
[23] J. Viennet, C. Audoin, and M. Desaintfucien, IEEE Trans.
|
|
Instrum. Meas. IM-21, 204 (1972). [24] H. Hellwig and H. E. Bell, Metrologia 8, 96 (1972). [25] F. L. Walls and H. Hellwig, Proc. 30th Annual Symp. on
|
|
Freq. Control (Electronics Ind. Assoc., Wash., D.C,
|
|
1976), p. 473.
|
|
[26] H. E. Peters, Proc. 32nd Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C, 1978), p. 469.
|
|
[27] H. T. M. Wang, Proc. 34th Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C, 1980), p. 364.
|
|
[28] E. M. Mattison, E.L. Blomberg, G.U. Nystrom, and R. F. C. Vessot, Proc. 33rd Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C, 1979), p. 549.
|
|
[29] D. A. Howe, F. L. Walls, H. E. Bell, and H. Hellwig, Proc. 33rd Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C, 1979), p. 554.
|
|
[30] M. Jardino, M. Desaintfuscien, R. Barillet, J. Viennet, P. Petit, and C. Audoin, Proc. 34th Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C, 1980),
|
|
p. 353. [31] H. A. Schuessler, Metrologia 7, 3 (1971).
|
|
[32] M. D. McGuire, Proc. 31st Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C, 1977), p. 612.
|
|
[33] D. J. Wineland, W. M. Itano, J. C. Berquist, and F. L. Walls, Proc. 35th Annual Symp. on Freq. Control (Electronics Ind. Assoc., Wash., D.C), to be published.
|
|
[34] H. G. Dehmelt, Adv. At. Mol. Phys. 3, 53 (1967). [35] D. J. Wineland, R. E. Drullinger, and F. L. Walls, Phys.
|
|
Rev. Lett. 40, 1639 (1978).
|
|
[36] W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt,
|
|
Phys. Rev. Lett. 41, 233 (1978).
|
|
|
|
19
|
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|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
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|
|
Performance of the Three NRC 1 -Meter CsVI Primary Clocks
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|
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A. G. Mungall, H. Daams, and J.-S. Boulanger
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Division of Physics, National Research Council, Ottawa, Ontario, Canada, K1A 0R6
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The performance of the three 1-m interaction length NRC primary cesium clocks, CsVIA, CsVIB,
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|
and CsVIC, is outlined for their initial year and a half of operation as primary clocks, which com-
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|
|
menced in December, 1979. Measurements of their systematic corrections made then and again early in
|
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|
1981 indicate only small changes, within the accuracy limit of ± 1.5 x lQ~^'-\ The frequencies of the
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|
|
three clocks compared with that of CsV remained within ± 2 x 10"''' despite certain problems concern-
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|
|
ing the electronics systems which became apparent during this test period and which limited their long-
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|
|
term frequency stability. These problems, which caused frequency shifts arising from spectral impuri-
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|
ties in the microwave exciting signal, have been partially corrected, with consequent improvement of
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NRC the agreement between all four
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|
|
primary clocks to better than 5 x 10"'^. The potential long-term
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|
|
frequency stability appears to be a few parts in 10'^.
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|
|
Key words: frequency stability; performance; primary cesium clocks; spectral impurities; systematic
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|
corrections.
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|
|
1. Introduction
|
|
When the CsVI clocks were designed early in 1976, the
|
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intent was to achieve a stability as good as that of the
|
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NRC long beam primary cesium clock, CsV, and an accu-
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|
racy only slightly less, in a unit much smaller in physical dimensions at a significantly lower cost [1-4]. It was also hoped that clocks embodying such a design might prove attractive from the point of view of later commercial exploitation, since their potential accuracy would be about •50 times better than that of currently available commercial clocks. Three cesium clocks were built of this design,
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as shown in Fig. 1, during 1977 and 1978, and began operation as secondary clocks late in 1978. As mentioned in an earlier publication [5], which outlined their salient design characteristics, certain difficulties arising from thermo-electric currents flowing in the magnetic shields and the aluminum interior support cylinder, and from mechanical distortions were encountered. The former were overcome by improved clock and room temperature control, and the latter by spring-mounting the ion pumps and the microwave excitation system.
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Following an initial test, evaluation, and adjustment
|
|
period, a complete accuracy evaluation was made of each
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Figure l. The three CsVI clocks. 21
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clock late in 1979. This was repeated early in 1981, and only minor alterations in the systematic corrections were
|
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observed. Since December, 1979, all three clocks have operated
|
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completely independently as primary standards, produc-
|
|
ing the scales of proper time PT(NRC CsVIA), PT(NRCCsVIB), and PT(NRC CsVIC). The relations between these three scales and UTC(NRC), which is based solely
|
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on CsV, have been reported at 10-day intervals to the Bureau International de VHeure.
|
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This paper will describe their performance during the first year and a half of their operation as primary clocks, based not only on their accuracy evaluations, but also on comparisons between their scales of proper time and
|
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UTC(NRC), and between UTC(NRC) and TA(NRC), and UTC(USNO), UTC(BIH), TA(NBS), and TA(PTB).
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2. Results
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2.1 Accuracy Evaluations
|
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It is essential in primary clock operation that the various systematic corrections such as the cavity phase difference, the second order Doppler shift, and the fre-
|
|
quency offset dependent on the direction of the C field remain constant. They should also be as small as possi-
|
|
ble, with magnitudes similar to that of the total clock uncertainty. The two complete evaluations so far performed on the CsVI clocks show that these two requirements have been met. None of the corrections exceeds 2 or 3 x 10"^"^, and each remains constant within several parts in
|
|
lO^'* except when known changes have been made or have occurred to some component of the clock.
|
|
The latter proviso is particularly applicable in the case of the C-field reversal effect, which appears sensitive primarily to changes in the form of the C field in the vicinity of the two microwave interaction regions. Such a sensitivity is to be expected on the basis of an analysis presented in a previous publication [6]. Measurements of
|
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the C-field uniformity, using the set of six axial coils
|
|
which excite the (4, -4) - (4, -3) transition, are performed regularly to check the constancy of this frequency
|
|
shift.
|
|
Measurements during the first year of operation, during 1980, disclosed unexpected instabilities in the microwave excitation systems which originated in all the
|
|
component units, the 5-90 MHz frequency multipHer, the 12.6 MHz frequency synthesizer, the step recovery diode
|
|
matching network, and the Gunn diode phase-locked frequency source. These all affected the spectral purity of the beam excitation signal and led to time-dependent frequency shifts. Modifications made to all these units have improved their performance, but further work is neces-
|
|
sary to attain consistently the long-term frequency stability of which the clocks are capable.
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2.2 Short-Term Frequency Stability
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Measurements of the short-term frequency stability of
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each of the CsVI clocks intercompared, or compared with
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|
CsV, indicate that for values of t between 2 and 10^ s,
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|
the value of ct(2, t) for any combination of the clocks can
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be described by the expression 4.6 x 10~^^t
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The
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|
value of ct(2, 10'^ s) is about 1.2 x 10
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|
or 8 x 10 per
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|
clock. The dependence of a on t is shown in Fig. 2.
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10''^
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'
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I
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10
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I
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1
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I
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mI I
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I
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I
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I
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10^
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10^
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V, SECONDS
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I
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lo''
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' 10*
|
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|
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Figure 2. The short-term frequency stability of the CsVI docks both intercompared and compared with CsV.
|
|
|
|
2.3 Long-Term Frequency Stability
|
|
The long-term frequency stability of the CsVI clocks is indicated in Fig. 3, which shows comparisons of their scales of proper time and UTC(NRC), based on CsV.
|
|
Also shown in the figure are comparisons of UTC(NRC) and TA(NRC) with UTC(BIH), UTC(USNO), TA(PTB)
|
|
and TA(NBS). The complete accuracy evaluations for both CsV and the CsVI clocks are indicated in Fig. 3 as well as the dates for a number of partial evaluations of the latter. Also shown are the times at which a variety of clock adjustments or equipment modifications were made. In a number of cases, slope changes, indicating frequency shifts, are evident at these times. The figure shows that throughout the measurement period the relative frequencies of CsV and the CsVI clocks were generally within ±2 x 10"^'^ despite recognized difficulties with the electronics systems. Subsequent to the 1981 CsVI evaluations, and after partial correction of these
|
|
difficulties, this value decreased to about 5 x 10^^"*.
|
|
During periods for which no adjustments or modifications were made the long-term relative frequency stability, a(2, t), drops below 1 x '10"", as indicated in Table 1. This table also shows that if the C-field frequency steering corrections required in primary clock operation are taken into account then the value of a(2, t) decreases to a few parts in 10''^.
|
|
Examination of the lower portion of Fig. 3 showing
|
|
comparisons between the NRC time scales based on CsV
|
|
and those of the BIH and other national laboratories indi-
|
|
cates that the frequency variations between these scales
|
|
are of the order of ±2 x 10"''^ with the sole exception of TA(NRC) - TA(PTB), which exhibits maximum changes of about ±1 X 10". These comparisons, based princi-
|
|
pally on LORAN C measurements, are subject to daily and
|
|
annual signal propagation delay fluctuations, but the latter appear to be appreciably smaller than the varia-
|
|
tions shown in the figure. All these variations are similar in magnitude to those measured for the CsVI clocks with
|
|
respect to CsV during a period when known causes existed to explain the CsVI frequency fluctuations. It
|
|
should therefore be possible to reduce the limits of the
|
|
fluctuations between the NRC primary clocks to values
|
|
significantly lower than those at present occurring between the scales of the various different laboratories.
|
|
3. Conclusions
|
|
The three 1-m NRC CsVI clocks, now in operation for
|
|
about two and a half years, provide first order accuracy
|
|
|
|
22
|
|
|
|
COMPARISONS BETWEEN UTC(NRC) AND PKNRC CsVIA), PKNRC CsVIB), AND PKNRC CsVIC)
|
|
CsVI CLOCK SYSTEMS FAILURES OR ADJUSTMENTS
|
|
i
|
|
CsVI PARTIAL RE-EVAUJATIONS I
|
|
|
|
MJD
|
|
Figure 3. Time scale comparisons between UTC(NRC) and PT(NRC CsVIA), PT(NRC CsVIB), and PT(NRC CsVIC) shown in the upper portion, and UTC(NRC) and TA(NRC) mth UTC(BIH), UTC(USNO), TA(NBS), and TA(PTB) in the lower portion.
|
|
|
|
NRC Table 1. Relative frequency stability for the
|
|
|
|
scales of proper time,
|
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|
|
unth and without corrections for C field steering of the clock frequencies
|
|
|
|
Time scales compared
|
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|
|
Meas. Period Total time,
|
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|
|
MJD to MJD
|
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|
|
days
|
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|
|
T
|
|
days
|
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|
|
a (2, t) X 10-15 Uncorrected Corrected
|
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|
|
CsVIA-CsV 44303 44354
|
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|
|
51
|
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|
|
17
|
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|
|
6.2
|
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|
|
2.2
|
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|
|
CsVIB-CsV 44583 44658
|
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|
|
75
|
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|
|
25
|
|
|
|
1.2
|
|
|
|
1.7
|
|
|
|
CsVIC-CsV 44301 44430
|
|
|
|
129
|
|
|
|
43
|
|
|
|
6.3
|
|
|
|
3.6
|
|
|
|
and frequency stability in a clock appreciably smaller
|
|
than CsV or other comparable primary standards. It is
|
|
likely that further improvements in the electronics systems will lead to the reahzation of a long-term stability of a few parts in 10^^.
|
|
References
|
|
[1] A. G. Mungall, R. Bailey, H. Daams, D. Morris, and C. C.
|
|
|
|
Costain, Metrologia 9, 113 (1973). [2] A. G. Mungall, H. Daams, D. Morris, and C. C. Costain,
|
|
Metrologia 12, 129 (1976). [3] A. G. Mungall and C. C. Costain, Metrologia 13, 105 (1977).
|
|
[4] A. G. Mungall, IEEE Trans. Instrum. Meas. IM-27, 330
|
|
(1978).
|
|
[5] A. G. Mungall, H. Daams, and J.-S. Boulanger, IEEE Trans.
|
|
Instrum. Meas. IM-29, 291 (1980). [6] A. G. Mungall, Metrologia 12, 151 (1976).
|
|
|
|
23
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Prospects for Cesium Primary Standards at the National Bureau of Standards
|
|
L. L. Lewis, F. L. Walls, and D. A. Howe
|
|
Time and Frequency Division, National Bureau of Standards, Boulder, CO 80303
|
|
An application of optical pumping, in conjunction with a number of design improvements, may per-
|
|
mit the development of a cesium primary standard vnth an accuracy an order of magnitude better than that of our present primary frequency standards, NBS-4 and NBS-6. Limitations to short-term stability, as well as possible errors in accuracy, are discussed.
|
|
Key words: atomic clock; atomic frequency standards; cesium frequency standard; light shift; optical
|
|
pumping.
|
|
|
|
1. Introduction
|
|
The United States' primary frequency standard, NBS6, was placed into service in 1975. This cesium standard
|
|
has an accuracy of about 8 x 10"^'*, long-term stability better than 1 x 10"^'*, and short-term stability of about
|
|
5 X 10"^^ T"^. Research in progress at NBS is directed
|
|
tovi^ards the design of a new cesium standard with an order of magnitude improvement in accuracy and longterm stability and a factor of two or three improvement in short-term stability. Much of this improvement may be obtained through the use of optical pumping state
|
|
preparation and fluorescence detection, and the rest of the advancement vdll come from a number of technological innovations in the clock system.
|
|
The accuracy of NBS-6 is limited in large part by microwave phase shifts associated with losses in the Ramsey cavity [1]. The results of the 1980 evaluation of NBS-6 are given in Table 1, clearly illustrating this fact.
|
|
|
|
The size of the apparent shift of the microwave resonance frequency is approximately
|
|
|
|
Av4>
|
|
|
|
(1)
|
|
|
|
where Acj) includes both end-to-end and distributed cav-
|
|
|
|
ity phase shift, and A v^^ is the microwave linewidth of the
|
|
central Ramsey feature. Since Av^ ~ 30 Hz, one concludes from Table 1 that A(J) ~ 3 x 10"^ radian. This is a
|
|
|
|
reasonable value for a cavity structure as large as the
|
|
|
|
one used in NBS-6 [2]. Assuming a linear dependence of
|
|
|
|
the distributed cavity phase shift upon position across
|
|
the microwave cavity window of ~ 1 x 10"^^ rad/mm [1,
|
|
|
|
2], it would be necessary to obtain retrace of the cesium
|
|
beam to within ~ 100 n-xn in order to ensure a frequency
|
|
|
|
error associated with the cavity phase shift of less than
|
|
|
|
We 10"^^.
|
|
|
|
believe that the use of optical pumping state
|
|
|
|
preparation and fluorescence detection techniques in a
|
|
|
|
cesium atomic beam frequency standard should make
|
|
|
|
Table 1. NBS-6 uncertainties, 1980 evaluation.
|
|
|
|
Source of Uncertainty
|
|
|
|
Bias {uy x 10^3) Uncertainty (x lO^^)
|
|
|
|
(a) Cavity Phase Shift (for one direction) (residual first-order Doppler Shift)
|
|
(b) Second-order Doppler
|
|
Shift
|
|
Pulling by neighboring transitions
|
|
Magnetic Field Effects (a) Offset due to finite field
|
|
(b) Magnetic field inhomogeneity (c) Majorana Transitions
|
|
Servo System Offset (a) Amplifier offsets (b) Second harmonic
|
|
distortion
|
|
RF Spectrum
|
|
Cavity Pulling
|
|
|
|
3.3 (typical)
|
|
-2.8
|
|
(typical) -hO.3
|
|
(typical)
|
|
+0.02
|
|
|
|
RMS error due to
|
|
systematic frequency biases
|
|
Random Uncertainty
|
|
|
|
0.80
|
|
0.10 0.20 0.02 0.02
|
|
?
|
|
0.1 0.2 0.1 0.01 0.87 0.15
|
|
|
|
25
|
|
|
|
such a precision retrace possible. In addition, different
|
|
microwave cavity structures than that used in NBS-6 may reduce the cavity phase shift dependence upon position, thereby relaxing the retrace requirement by as much as an order of magnitude.
|
|
The effect of Majorana transitions on the accuracy of Cs standards is not clear. Various authors [3] have suggested that they may produce uncertainties as large as one part in 10^^. If optical pumping is used for state preparation and detection, such Majorana transitions
|
|
should not occur, since a uniform C-field strength can be maintained throughout the clock. In addition, by using laser techniques, it should be possible to measure Majorana transitions which might occur.
|
|
Optical pumping may reduce other sources of uncer-
|
|
tainty as well. If only a single magnetic sublevel is
|
|
prepared, there will be no Am^ = 0 neighboring transi-
|
|
tions which would shift the central resonance. This would
|
|
permit a much lower value of C-field, which would relax restrictions on measurement of the finite field, as well as
|
|
reduce the effect of magnetic field inhomogeneities and magnetic field changes with time.
|
|
The other contributions to uncertainty listed in Table 1
|
|
are not considered to be serious limitations to accuracy
|
|
at the 10"'^ level, assuming some reasonable improvements in electronics and measurement techniques are made. However, as discussed below, the introduction of optical pumping will create new sources of error which must be considered.
|
|
|
|
2. Optical Pumping and Fluorescence
|
|
Detection
|
|
|
|
The development of high performance, cw, single-mode diodes for the communications industry has fortunately provided an optical pumping source appropriate for use in atomic frequency standards. The linewidth, intensity noise, frequency noise, and wavelength tuning characteristics of these devices make them very attractive for this purpose [4]. At the present time, it is reasonable to expect laser diodes to operate tuned to an atomic transition for months at a time.
|
|
|
|
The first use of laser diodes to optically pump a cesium beam atomic clock was made by Arditi and Picque [5]. They used a single GaAlAs laser tuned to the D2 line of Cs (852 nm) in order to pump atoms into one of the
|
|
F =3, 4 ground-state hyperfine levels (Pig. 1). Detection
|
|
of a microwave transition within the Ramsey cavity was
|
|
accomplished by fluorescence detection using the same
|
|
|
|
laser.
|
|
|
|
The work at the National Bureau of Standards (NBS)
|
|
|
|
has moved in a somewhat different direction, requiring
|
|
|
|
more than one laser. It is possible to pump nearly every
|
|
|
|
Cs atom in an atomic beam into a single magnetic sub-
|
|
|
|
F=3 ^ level [6]. If one laser is tuned to • the 6
|
|
|
|
1/2
|
|
|
|
6 ^Pa^ F'-^ transition, and a second laser is
|
|
|
|
^ tuned to the 6 1/2 =4
|
|
|
|
6
|
|
|
|
F'=4 transition with
|
|
|
|
plane electric polarization parallel to a weak magnetic
|
|
|
|
F field (-rr-polarization), only atoms in the =4, m^-^O sub-
|
|
|
|
level of the ground state will remain unaffected. This
|
|
|
|
selection rule is clear when one notes that the Clebsch-
|
|
|
|
Gordon coefficient <Fjm,Fmj\F'mf> - <F100|
|
|
F0> = 0, where j is the angular momentum of the pho-
|
|
|
|
ton. Eventually, most of the atoms will be pumped into
|
|
|
|
this magnetic sublevel. Alternatively, a similar arrange-
|
|
ment can pump atoms into the F =3, mp -0 state.
|
|
|
|
Fluorescence detection can be performed with a third
|
|
F laser which is tuned to either the =4 F' =5 or the
|
|
|
|
Mp= -4-2 0 2
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
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|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
253 MHz
|
|
|
|
5-1
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
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|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
203 MHz
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
152 MHz
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
4 6^P3/2 3 F'=2
|
|
|
|
852 nm
|
|
|
|
M = -4-2024
|
|
|
|
I
|
|
|
|
I
|
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|
|
I
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I
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I
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I
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I
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|
|
I
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|
|
|
I
|
|
|
|
9.19263177 GHz
|
|
II
|
|
|
|
F=3
|
|
|
|
6^Si/2
|
|
|
|
Figure l. Term diagram for Cs.
|
|
|
|
-
|
|
|
|
F -S
|
|
|
|
F' -2 transition. In these two cases (with
|
|
|
|
F ^ appropriate polarization of the =B F' =2 laser light
|
|
|
|
to avoid pumping into the
|
|
|
|
= ±3 sublevels), atoms in
|
|
|
|
the excited state return to the original ground-state
|
|
hyperfine level. Thus, a large number of fluorescence
|
|
|
|
photons (limited by excited-state energy separations)
|
|
may be obtained from each atom in the atomic beam. This
|
|
|
|
technique should permit unity quantum detection effi-
|
|
|
|
ciency, even if the light collection efficiency is consider-
|
|
|
|
ably less than one. However, as discussed below, there
|
|
may be systematic effects which would make this detec-
|
|
tion method undesirable. In this case, it is still possible to use a laser tuned to a pumping transition, and take
|
|
|
|
care to obtain a high collection efficiency at the detector.
|
|
An additional advantage a pumping transition provides in
|
|
|
|
detection is that every atom is weighted equally regard-
|
|
less of velocity, which may provide immunity from certain systematics. On the other hand, detection by
|
|
|
|
fluorescence on a cycling transition produces a relatively
|
|
|
|
larger signal for slower atoms which remain in the laser
|
|
beam longer, which would increase the effective
|
|
|
|
microwave Q. Still another advantage of optical pumping is that it should be possible to operate atomic beams in
|
|
|
|
opposite directions simultaneously without interference.
|
|
|
|
This would permit direct measurement of retrace, as well as very rapid modulation of beam direction (or even con-
|
|
|
|
tinuous operation of two beams) for purposes of cancella-
|
|
A tion of cavity phase shift. final consideration in the use
|
|
of fluorescence detection is that the laser beam can be made to intersect the atomic beam at a slight angle,
|
|
|
|
thereby selecting low velocity atoms. This would cause
|
|
|
|
an increase in the microwave transition Q, with some accompanying loss of signal. This result is a consequence
|
|
|
|
of the Doppler shift, which changes the effective velocity distribution of the cesium beam. As further experiments
|
|
|
|
are performed, the relative merits of these various detec-
|
|
|
|
tion methods will become clearer.
|
|
|
|
Using values of atomic beam current Ib -1.0 xiA (6 X 10^ atoms/s) and microwave transition Q ~ 10^, it should be possible to obtain stabilities of — 1 x 10~^^
|
|
T~^, even if a pumping transition is used for detection purposes. The high beam current suggested here would
|
|
|
|
come partially from the increased number of useful
|
|
|
|
cesium atoms (a factor of 8 more than that of NBS-6,
|
|
|
|
26
|
|
|
|
through optical pumping of all magnetic sublevels), and
|
|
partially from new oven design. A reflux-type oven is
|
|
presently under consideration.
|
|
|
|
3. Additional Uncertainties and Biases
|
|
|
|
Perhaps the most serious source of frequency uncer-
|
|
|
|
tainty introduced by optical pumping techniques is that
|
|
|
|
of near-resonant light shifts [7, 8]. Although it should be possible to prevent stray laser light from entering the
|
|
|
|
microwave region, fluorescence hght from the atoms will
|
|
|
|
pass through the cavity, and interact with atoms in the
|
|
|
|
"C" region, changing the ground-state hyperfine split-
|
|
|
|
ting shghtly. The form of this light shift is dispersive,
|
|
|
|
but averaging over excited-state hyperfine levels and in-
|
|
|
|
cluding Doppler shifts associated with the MaxwelHan
|
|
|
|
velocity distribution in the atomic beam, gives a nonzero
|
|
|
|
value for the shift. Preliminary calculations have been
|
|
made at NBS [9] for the frequency shift from fluores-
|
|
cence light for pumping by two lasers of -ir-polarization,
|
|
|
|
with the C-field transverse to the atomic beam direction,
|
|
|
|
and including the effect of the tensor light shift [8].
|
|
|
|
The computations, assuming lasers of equal power
|
|
driving the F =4^F' =4andF = 3^F' = 4 transitions
|
|
|
|
in the pumping region, give a light shift of approximately
|
|
|
|
4 Hz for a power flux of 1 ixW/cm- at the site of the
|
|
cesium atom in the C-field region. A simple computer cal-
|
|
|
|
culation gives ten as the average number of photons em-
|
|
|
|
itted per atom in this pumping scheme. Referring to
|
|
|
|
Fig. 2, reasonable values of the clock dimensions would
|
|
|
|
be li = I2 ^ h = 50 cm, and L = 200 cm. Assuming a
|
|
|
|
beam flux of 6 x 10^ atoms/s at the detection region, and
|
|
|
|
mm a free aperture of 2
|
|
|
|
everywhere in the cesium
|
|
|
|
beam, the total fluorescent power arriving at the first
|
|
|
|
window of the Ramsey cavity from the pumping region
|
|
would be about 2 x 10"^ jo-W/cm^. This gives a fractional
|
|
frequency shift of ~ 9 x 10"^^, which is comparable to
|
|
|
|
the desired accuracy. Additional coUimation of the atomic
|
|
|
|
beam before the pumping region would reduce this
|
|
|
|
predicted light shift by a factor of ten or more.
|
|
|
|
Nevertheless, a more careful calculation of the effect will
|
|
|
|
be made, including the effective velocity distribution as-
|
|
|
|
sociated with cycling fluorescence detection, and includ-
|
|
|
|
ing the shift caused by light originating in the detection
|
|
|
|
region. In addition, versions of optically pumped fre-
|
|
|
|
quency standards being considered contain provision for
|
|
|
|
measurement of the light shift.
|
|
|
|
A
|
|
[Beam
|
|
|
|
^3
|
|
>< ^ >
|
|
A
|
|
/\
|
|
|
|
Cs Oven
|
|
|
|
Pump
|
|
Laser
|
|
|
|
Ramsey
|
|
Cavity
|
|
|
|
Detect ion Laser
|
|
|
|
Figure 2. Schematic of Cs atomic beam frequency standard.
|
|
|
|
A second source of trouble associated with the laser
|
|
optical pumping is deflection of the atomic beam through photon recoil. The deflection is about 1.6 x 10"^ rad/photon for an average atomic velocity of ~ 200 m/s.
|
|
|
|
and proportionately greater for slower velocities. If the
|
|
Cs beam is irradiated symmetrically on two sides, an expansion of the atomic beam should occur, with magnitude
|
|
~ 5 X 10"^ rad. With the same assumptions used above
|
|
to estimate the limitations imposed by beam retrace, this
|
|
should give an uncertainty in frequency considerably less than 10-1^
|
|
Still another correction to the Cs microwave frequency,
|
|
not unique to optical pumping, but which has not been
|
|
fully considered in the past, is the light shift caused by blackbody radiation. The ac Zeeman shift of the groundstate hfs of Cs, due to the magnetic field of the black-
|
|
body radiation is only ~ 10"^^ [11]. However, the light
|
|
shift associated with the rms electric field of the blackbody radiation is considerably larger [10]. The approxi-
|
|
K mate magnitude of the shift correction at T = 300 is
|
|
about
|
|
|
|
8Vss
|
|
|
|
-
|
|
|
|
1.8
|
|
|
|
X
|
|
|
|
-14
|
|
10
|
|
|
|
(2)
|
|
|
|
Vhfs
|
|
|
|
The sensitivity of an anticipated new cesium primary standard would be adequate to measure this effect in a
|
|
suitably designed apparatus.
|
|
|
|
4. Conclusion
|
|
|
|
Optical pumping techniques may improve both the ac-
|
|
curacy and short-term stability of Cs primary frequency standards. The greatest anticipated improvement comes
|
|
from better retrace upon beam reversal. New problems
|
|
associated with laser diode optical pumping will require serious consideration, but are not seen as major obstacles to the design of an improved standard.
|
|
|
|
The authors wish to thank their colleagues in the Time and Frequency Division for many fruitful discussions. The contributions of D. Wineland, E. Smith, and D. Glaze were especially helpful.
|
|
References
|
|
|
|
[1] D. J. Wineland, D. W. Allan, D. J. Glaze, H. W. Hellwig,
|
|
and S. Jarvis, Jr., IEEE Trans. Instrum. Meas. IM-25,
|
|
|
|
453 (1976). [2] R. F. Lacey, Proc. 22nd Annual Symp. on Frequency Con-
|
|
trol, U.S. Army Electronics Command, Ft. Monmouth,
|
|
|
|
NJ, 545 (1968).
|
|
[3] G. Becker, IEEE Trans, Instrum, Meas. IM-27, 319 (1978);
|
|
D. W. Allan, H. Hellwig, S. Jarvis, D. A. Howe, and R. M. Garvey, Proc. 31st Annual Symp. on Frequency Con-
|
|
trol, Ft. Monmouth, NJ, 555 (1977); S. Urabe, K. Nakafiri,
|
|
Y. Ohta, M. Kabayashi, and Y. Saburi, IEEE Trans. In-
|
|
|
|
strum. Meas. IM-29, 304 (1980). [4] L. L. Lewis and M. Feldman, Proc. 35th Annual Symp. on
|
|
Frequency Control, U.S. Army Electronics Command, Ft. Monmouth, NJ (1981) 612.
|
|
[5] M. Arditi and J.-L. Picque, J. Phys.-Lett. (Paris) 41, L-379 (1980); see also M. Arditi, these proceedings.
|
|
[6] This method was made known to us by L. Cutler. See also H. J. Gerritsen and G. Nienhuis, Appl. Phys. Lett. 26, 347
|
|
|
|
(1975).
|
|
|
|
We [7]
|
|
|
|
are grateful to A. Brillet for emphasizing the seriousness
|
|
|
|
of this systematic to us.
|
|
|
|
[8] B. S. Mathur, H. Tang, and W. Happer, Phys. Rev. 171, 11
|
|
|
|
(1968); W. Happer and B. S. Mathui-, Phys. Rev. 163, 12
|
|
|
|
(1967).
|
|
[9] E. Smith, private communication.
|
|
A [10] W. M. Itano, L. L. Lewis, and D. J. Wineland. Phys. Rev.
|
|
|
|
25, 1233 (1982).
|
|
[11] T. F. Gallagher and W. E. Cooke, Phys. Rev. Lett. 42, 835
|
|
|
|
(1979).
|
|
|
|
27
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
A Cesium Beam Atomic Clock with Laser
|
|
Optical Pumping, as a Potential Frequency Standard
|
|
|
|
M. Arditi
|
|
Institut d'Electronique Fondamentale*, Universite Paris XI, Bat. 220, 91405 Orsay, France
|
|
A passive microwave cesium beam resonator using optical pumping and optical detection, with a cw
|
|
tunable GaAs diode laser, has been realized. The "0-0 clock transition" is detected through a change in the intensity of the fluorescence of the cesium beam. Experimental recordings of the Ramsey pattern
|
|
agree with a Maxwellian distribution of atomic velocities. Results of prehminary tests, to an accuracy of a few parts in 10", show good potential for a frequency standard of higher accuracy.
|
|
Key words: atomic clock; cesium beam; frequency standard; laser diode; optical pumping.
|
|
|
|
1. Introduction
|
|
With a cesium beam frequency standard of the RabiRamsey type, an accuracy better than 10~^^ in the reali-
|
|
zation of the second appears to be a realistic probability [1]. This accuracy is limited mainly by second-order Doppler-shift and cavity phase-shift w^hose estimation depends on a precise measurement of the velocity distri-
|
|
bution of the atoms in the beam [2]. The purpose of this paper is to describe a cesium beam
|
|
atomic frequency standard where optical pumping could, perhaps, further extend the limits of accuracy due to
|
|
these effects.
|
|
As early as 1950, A. Kastler [3] had proposed to replace the Stern-Gerlach magnets in a Rabi classical atomic beam magnetic resonance apparatus by "optical pumping," to create and detect differences in the Zeeman sublevel populations of the ground state of the alkali atoms
|
|
A [4]. successful application of these principles was ob-
|
|
tained in a **''Rb atomic beam to measure accurately the
|
|
hyperfine structure separation of the ground state [5]. In that experiment, optical pumping was achieved using the isotopic shift of the '^^Rb and *^''Rb resonance lines emitted by spectral lamps. However, limited by a weak signal to noise ratio of the detection, the device could not be used conveniently as a practical frequency standard.
|
|
The advent of stable, monochromatic and tunable laser sources (diode lasers or dye lasers) in the near infra-red, had raised the hope of increasing the signal to noise ratio in optically pumped atomic beam clocks. After the successful experiments of J.-L. Picque on hyperfine pumping of a cesium beam using a GaAs laser diode [6], an attempt was made to set up an optically pumped cesium beam clock with optical detection. The preliminary results were described in a brief report [7]. In this paper more details are given on the experimental procedure and on the potentialities for a fully developed frequency standard.
|
|
2. Optical Pumping of a Cesium Beam
|
|
The experimental set-up is shown schematically in Fig. 1. In region A, optical pumping increases the popula-
|
|
*Laboratoire associe au C.N.R.S.
|
|
|
|
tion difference between the F = 4 and F — S levels of the
|
|
ground state of cesium atoms. In region C, microwave in-
|
|
teraction takes place, and in region B the microwave
|
|
resonance is detected with a photocell by a change in the intensity of the beam's fluorescence.
|
|
In this device, the atomic beam is axially symmetrical, and the velocity distribution of the cesium atoms is the same across the beam since there is no spatial selection
|
|
A as with the magnet, thus reducing considerably the
|
|
problem of the spatially distributed cavity phase-shift [8]. Moreover, the device can be made completely reversible by placing a cesium oven at each end, thus simplifying the retrace measurement of the residual cavity phase-shift. Also, as will be seen later, because of the high spectral density of the laser light, the cesium atoms wall all be pumped with the same efficiency, regardless of their velocity, so that the velocity distribution will be broad, very close to a Maxwell-Boltzmann distribution and thus the second-order Doppler-shift can be more
|
|
easily evaluated.
|
|
|
|
PHASE DETECTOR
|
|
|
|
MOD
|
|
2 KHz
|
|
|
|
192 MHz
|
|
|
|
RECORDER
|
|
|
|
FREQUENCE CONTROL
|
|
|
|
® [B. ^..s.°y
|
|
|
|
GaAs LASER
|
|
|
|
1.2,3 PHOTOCELLS
|
|
|
|
Figure l. Cesium beam resonator with optical pumping and
|
|
optical detection.
|
|
|
|
29
|
|
|
|
The time evolution for the population of the ground state hyperfine Zeeman levels of cesium atoms has been previously analyzed for the case where a cesium beam is optically pumped under different conditions of polarization, either with a weak monochromatic laser light or with the resonant light from a spectral lamp filtered by a
|
|
|
|
cesium cell [9].
|
|
|
|
With cesium spectral lamps and cesium filter-cells, no good experimental results could be obtained in population changes in a cesium atomic beam, although very good
|
|
signal to noise ratio resulted in the optical detection of the 0-0 transition in a gas cell [10]. This failure could be
|
|
attributed perhaps to a lack of pumping light due to too much light absorption by the filter-cell.
|
|
|
|
More successful results were achieved with a semiconductor laser diode (type LD-33, from Laser Diode Lab. Inc.) originally intended for pulse-operation and adapted by J.-L. Picque for cw, single mode operation in
|
|
|
|
a temperature-stabilized cryostat at about 25 K.
|
|
|
|
mA For an injection current of 200
|
|
|
|
this laser diode
|
|
|
|
delivers a few milliwatts of power, and the output
|
|
|
|
wavelength is coarsely adjusted in the vicinity of the
|
|
|
|
cesium D2 resonance jine (852.1 nm) by changing the tem-
|
|
perature (about 2.4 A per °C) and finely tuned to one of
|
|
|
|
the hyperfine components by varying the injection
|
|
current (about 200 MHz per mA). The phase-jitter of the
|
|
|
|
laser light can be reduced considerably by locking the
|
|
|
|
frequency of the laser to an external Fabry-Perot resona-
|
|
|
|
tor. More details on the operation of the laser diode and
|
|
|
|
cryostat can be found in Ref. [11]. By sweeping the
|
|
|
|
piezo-crystal of the Fabry-Perot with a dc voltage ramp,
|
|
the laser frequency can be tuned over a wide range. A
|
|
|
|
photocell, under the cesium beam, is used to detect the
|
|
|
|
fluorescence of the beam.
|
|
|
|
The cesium atomic beam is produced in a stainless steel
|
|
m vacuum chamber about 1.5 long, fitted with several
|
|
|
|
glass windows to admit the light of an external laser
|
|
|
|
diode. The collimator of the cesium oven is an array of
|
|
|
|
about 185 nickel tubes (diam. = 0.25 mm, length = 10
|
|
|
|
mm mm) inside a 6
|
|
|
|
diam. cylinder. The directivity of the
|
|
|
|
beam being rather poor at the oven exit, the cesium beam is further collimated by several apertures (diam. -
|
|
8 mm) distributed along the axis, and resulting in a beam
|
|
|
|
divergence from the axis of less than 1 degree. The aper-
|
|
|
|
ture supports are coated with lamp-black to act as an ef-
|
|
|
|
ficient getter for diverging cesium atoms, and a movable
|
|
|
|
stop is provided in front of the oven to check that the
|
|
detected signals are due to the atomic beam and not to some residual cesium vapor. At the end, an ion detector can be placed to give a measurement of the cesium
|
|
atomic density in the detection region, which typically for an oven temperature of 96 °C is of the order of 2 x 10^ atoms per cm^. Right under the cesium beam, in the
|
|
|
|
regions of illumination, silicon photocells are placed in
|
|
shallow cups (to protect them from cesium deposits) to
|
|
|
|
detect the fluorescence of the beam.
|
|
|
|
Figure 2(b) shows a recording of the derivatives of the
|
|
absorption lines originating on the F = 3 level and
|
|
detected by the fluorescence of the beam as the laser diode was swept in frequency. The line-width of each
|
|
hyperfine component is about 50 MHz. Similar results
|
|
F were obtained for transitions originating on the = 4
|
|
|
|
level.
|
|
|
|
Due to selection rules which allow only AF = 1,
|
|
^ ^nif = 0, ± 1 transitions to take place, atoms in the
|
|
ground state undergoing 3 —> 2 or 4 5 transitions can
|
|
only return to their original level and the total population
|
|
of these ground levels should not change due to these
|
|
|
|
155
|
|
|
|
153 I ma
|
|
|
|
Figure 2. a) Energy levels for cesium D2 transitions;
|
|
F h) Derivatives of D2 absorption lines originating on = 3
|
|
level, recorded by fluorescence of a cesium, beam.
|
|
|
|
two transitions. However, as was shown in Ref. [9] when detailed balancing of the populations of all the Zeeman sublevels is carried out, a population difference can
|
|
appear between the F = 3, mp = 0 and F = 4, mp = 0
|
|
levels, even though the overall population of the ground
|
|
level should not change.
|
|
|
|
To study in detail these effects, the set-up of Fig. 1 was completed by placing a rotating light-chopper in front of the pumping window. Without microwave excitation, by alternatively pumping the cesium beam on and
|
|
off, the populations are redistributed in the various Zee-
|
|
man sublevels, and an unmodulated probe beam from the
|
|
laser can be used to detect the total population changes
|
|
by monitoring the modulation of the beam fluorescence.
|
|
|
|
Figure 3(a) shows such a recording obtained by sweep-
|
|
|
|
ing the laser frequency. It can be seen that the largest
|
|
3^3 signal is obtained with the laser diode tuned to the
|
|
|
|
transition frequency. It is interesting to note also that a
|
|
|
|
3^2 distorted signal is detected at the
|
|
|
|
transition
|
|
|
|
although, according to the selection rules, the total popu-
|
|
F lation of the = 3 level should not change. Similar
|
|
recordings were obtained with the laser tuned to the fre-
|
|
F quencies of the transitions originating on the = 4 level.
|
|
Changing the polarization of the laser light from linearly to circularly polarized, in all possible combinations for pumping or detecting, did not change significantly the signal shapes or magnitudes and it is finally simpler to use the light as it comes directly from the laser diode.
|
|
|
|
Since there is no saturation with the laser power
|
|
|
|
involved in these experiments, it is easy to compute the
|
|
relative change of fluorescence in the detection region B
|
|
|
|
produced by optical pumping of the cesium beam in
|
|
|
|
region A: here, it is about 7 percent, for the value of Igt
|
|
|
|
corresponding to experimental conditions {h = pumping
|
|
|
|
laser intensity: 6 x 10^^ photons /sec, and t = pumping
|
|
|
|
A time illumination: about 50 microseconds).
|
|
|
|
dual fre-
|
|
|
|
quency optical pumping scheme, with two lasers, has also
|
|
|
|
30
|
|
|
|
3-3
|
|
|
|
Figure 3. a) Optical detection of population change in F = 3
|
|
level produced by optical pumping of cesium beam, b) Optical detection of 0-0 microwave transitioyi.
|
|
|
|
been suggested, by which all of the atoms could be
|
|
F pumped into the = Z, nip = 0 (or = 4, rrip = 0) level
|
|
|
|
[12].
|
|
|
|
With the same experimental set-up, if in addition the microwave cavity is excited at the 0-0 frequency, i.e., 9192 , . . . MHz, it is found that the signals previously recorded in Fig. 3(a) are reduced by about 1/7 of their value, indicating that the change of fluorescence produced by the microwave interaction is about 1 percent of the total fluorescence of the cesium beam in B. This is also in agreement with the value given by a simple linear
|
|
theory.
|
|
|
|
To increase the signal to noise ratio of the optical
|
|
detection of the 0-0 transition, of interest in atomic clocks, the experimental set-up was modified as follows:
|
|
|
|
The light-chopper is removed and a low frequency
|
|
|
|
modulation is applied to the frequency of the microwave
|
|
A oscillation. maximum signal is obtained in photocell B
|
|
|
|
when the microwave frequency is set to the side of max-
|
|
|
|
imum slope of the 0-0 resonance curve. With the
|
|
|
|
microwave frequency fixed at this value, the laser diode
|
|
|
|
is swept in frequency and the signal out of photocell B is
|
|
|
|
recorded with a synchronous detector. Figure 3(b) shows
|
|
|
|
such a recording (similar results were obtained for laser
|
|
|
|
frequencies corresponding to transitions originating on
|
|
|
|
F the = 4 level). Here again there is a predominance of
|
|
|
|
3^3 signal at the
|
|
|
|
transition frequency and also an
|
|
|
|
unstable and peculiar shape signal from the 3 —» 2 transi-
|
|
|
|
tion frequency. In this 0-0 detection, the width of the
|
|
|
|
laser frequency range corresponds to the width of the
|
|
|
|
absorption lines in the cesium beam, about 50 MHz.
|
|
|
|
In conclusion: from these experiments it appears that the laser frequency giving the largest signal in the optical detection of the 0-0 transition is the frequency of the
|
|
3^3 transition, although, as we shall see later, the 3
|
|
4 transition frequency gives a better signal to noise ratio of the detection (in most of these experiments, the pho-
|
|
|
|
ton flux collected by fluorescence by the photocell in B was of the order of 5 x 10^*^ photons/sec).
|
|
For applications to atomic frequency standards, it is much better to lock the laser frequency directly to one of the absorption lines of the cesium beam itself [11]. As shown in Fig. 2(b), the derivative of these absorption Hnes are narrow-width S curves with a well defined cross-over which can be used for locking the laser frequency, and this was done in the following experiments.
|
|
|
|
3. Optical Detection of the 0-0 "Clock
|
|
Transition"
|
|
|
|
The experimental set-up of Fig. 1 was modified as follows: the laser frequency was set to correspond to one of the absorption lines of the cesium beam and was slightly frequency modulated (at a 3 kHz rate, for example). The modulated fluorescence of the cesium beam was detected
|
|
A by a photocell in feeding a phase detector. The output
|
|
of this phase detector controls the current of the laser
|
|
|
|
diode, thus locking the laser to the absorption frequency
|
|
of the cesium beam (see also Fig. 5).
|
|
|
|
The microwave cavity was of the Ramsey-type with os-
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|
|
|
cillating fields separated by a distance L. Circular holes
|
|
|
|
mm (8
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|
|
|
diam.) were provided at cavity ends for the pas-
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|
|
|
sage of the atomic beam. This cavity was made of a rec-
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|
|
|
tangular waveguide operating in a TEoi^v mode and is
|
|
|
|
resonant for a length equal to N\J2. Experimentally
|
|
two different cavities have been used: one with L = 21.5
|
|
|
|
cm (A^ = 14) and the other with L = 36.5 cm (A^ = 20), in
|
|
|
|
order to compare the experimental resonant curves with
|
|
|
|
the theory. The cavity was finely tuned to resonance
|
|
H E with a - waveguide tuner in the cavity feed.
|
|
|
|
The uniform magnetic field in region C was produced
|
|
by a U shaped electromagnet of Conetic metal. The
|
|
whole assembly, cavity and electromagnet, was placed in-
|
|
side a cylindrical magnetic shield of |jL-metal which was demagnetized by means of a 50 Hz ac current. The distri-
|
|
|
|
bution of the residual magnetic field inside the cavity was measured with a Hall effect magnetometer probe.
|
|
The mean value of the field could be obtained also, in operation, by inducing Zeeman low frequency transitions with two coils placed at the cavity ends, which at reso-
|
|
nance perturbed the 0-0 detected signal.
|
|
A photocell in B detected the change of fluorescence of
|
|
the cesium beam when the 0-0 transition was induced by microwave resonance. To study the shape of the 0-0 resonance curve, the microwave frequency was swept slowly around the resonance frequency. By modulating, at low frequency, the frequency of the microwave excitation, the output of a phase detector fed by photocell B gave a dc signal, the polaiity of which depended on the relative position of the microwave excitation and the 0-0 resonance frequencies. By sweeping the exciting frequency
|
|
this signal gave the derivative of the resonance curve.
|
|
An experimental curve is shown in Fig. 4 for a cavity with 1' = 1 cm and L = 21.5 cm (f = length of the oscillating field region, and L = distance between the two
|
|
separated oscillating fields), and an oven temperature of
|
|
|
|
about 85 °C.
|
|
|
|
According to Ramsey [13] the separated oscillating fields transition probability for a cesium atom in the
|
|
beam, with velocity v, is:
|
|
|
|
P=
|
|
|
|
sin2(25T)cos2[(coo
|
|
|
|
-
|
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|
|
a))L/2i'] ,
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|
|
(1)
|
|
|
|
where b the Rabi nutation frequency, is proportional to the square-root of the microwave power in the cavity, (ai the Bohr resonant frequency, co the excitation frequency,
|
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|
|
31
|
|
|
|
Figure 4. Experimental derivative of Ramsey pattern of cesium, beam, resonator tvith optical pumping by laser (solid curve) and theoretical values (dots) for Maxwellian distribution of atomic velocities (sweep speed: 16 Hz Is; recorder time
|
|
constant: 3 s).
|
|
|
|
and T the time the atom spends in each end of the cavity. Assuming the usual Maxwellian velocity distribution
|
|
for effusive beams:
|
|
|
|
/(?;)=
|
|
|
|
2( V 3/a4) exp (
|
|
|
|
-v Va^) ,
|
|
|
|
(2)
|
|
|
|
where a is the most probable velocity in the atomic beam, a = {2kT/m)^ {ni, mass of the cesium atom; T,
|
|
|
|
temperature of the cesium oven), the transition probabil-
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|
|
ity averaged over this velocity distribution is given by:
|
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|
|
<P >
|
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|
|
— " y''sm-\
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|
COS"
|
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|
an
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|
2ay
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|
|
dy (3)
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|
|
with
|
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|
|
y = via
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|
|
(4)
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|
|
|
<P> Near resonance, the derivative of
|
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|
|
versus frequency
|
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|
|
reduces to:
|
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|
(5)
|
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|
|
dj
|
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|
|
a
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|
|
mw +
|
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|
|
-
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|
(x
|
|
|
|
a
|
|
|
|
-il/2)K'{x),
|
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|
|
with X —
|
|
|
|
~ (oo)L/a and K'ix)
|
|
|
|
e~"^ y-sinixly) dy.
|
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|
|
(6)
|
|
|
|
On Fig. 4 such a theoretical curve has been plotted for the following values of the parameters: f = 1 cm, L 21.5 cm, a = 213 m/sec and 2b ( /a = 2.0 (corresponding
|
|
to a microwave signal power slightly over that for op-
|
|
timum transition probability) and vdth the ordinate of
|
|
|
|
the curve normalized to coincide with the maximum of
|
|
the experimental curve. The agreement between the experimental curve and the computed points is quite good, and gives evidence of a broad Maxwellian distribution of velocities in the beam. The frequency width between the central peaks of the derivative curve is about 500 Hz and
|
|
320 Hz for the microwave cavities with lengths L = 21.5 cm and 36.5 cm, respectively.
|
|
|
|
The shape of the resonance curve in this experiment is different from the one obtained in the optical pumping of a rubidium beam with spectral lamps [5] where there was a line-narrowing due to an enhanced contribution of the slower atoms to the overall signal [4]. This is probably due to the fact that the spectral density of the monochromatic
|
|
|
|
laser radiation is about 10^ times higher than for a spectral lamp, so that the efficiency of optical pumping is about the same for all the atoms, regardless of their transit time across the light beam. However, the lack of this resonance narrowing with laser pumping is more than compensated by the large increase in the signal to noise ratio (SIN) of the detection in this case and this makes the device attractive for atomic clock applications.
|
|
|
|
In the present experiments, the SIN is limited by the
|
|
|
|
noise due to residual phase-jitter of the laser diode. In
|
|
|
|
this respect, it was observed that the SIN was very bad
|
|
|
|
when locking the laser frequency to the 3 2 absorption
|
|
|
|
3^4 line of the cesium beam, and better with the
|
|
|
|
than
|
|
|
|
3^3 with the
|
|
|
|
transition. This effect may have been in-
|
|
|
|
^ ^ strumental, the slope of the S curve (Fig. 2(b)) for the
|
|
3-^4 transition being smaller than for the 3 2 or 3
|
|
|
|
3 transitions. Improvement in the SIN could be obtained
|
|
|
|
by increasing the laser intensity at the pumping region,
|
|
|
|
and by increasing the bandwidth of the amplifier and the
|
|
|
|
loop gain of the laser frequency servo. Also electro-
|
|
|
|
optical devices could be used to reduce amplitude noise of
|
|
|
|
the diode laser. Further work is contemplated in that
|
|
|
|
direction.
|
|
|
|
4. Operation as an Atomic Clock
|
|
4.1 Experimental Set-Up
|
|
Referring to Fig. 5, the microwave excitation signal is
|
|
synthesized from a stable 5 MHz voltage-controlled
|
|
quartz oscillator (H.P. 107 BR). The error signal from the phase detector acts on a voltage-variable capacitor to lock the frequency of this oscillator to the atomic transi-
|
|
tion. The output of the 5MHz oscillator is compared with
|
|
the frequency of a commercial cesium-beam frequency standard (H.P. 5061 A) either by frequency multiplica-
|
|
tion and counting, or in a phase comparator. In this way
|
|
the precision resetability of the clock and its accuracy could be checked versus various parameters such as: magnetic field, rf power, cavity tuning, rf modulation, laser light intensity or polarization, oven temperature, servo-gain, etc.
|
|
However, in these preliminary measurements, the electronics and the mechanical assembly were not sufficiently developed for measurements of 2nd-order Doppler shift or cavity phase-shift of the order of 10"^^ to 10"^"^. Since the commercial standard for frequency comparison has a limited accuracy of ±2 x 10"^\ and with the inclusion of
|
|
various biases in the electronics, it is believed that the
|
|
absolute accuracy of the measurements in these first tests was perhaps no better than ±3 x 10"^^ Also, since the SIN could probably be improved considerably with further work on the laser servo, the emphasis of the measurements was mostly on the accuracy of the clock rather than on short-term stability. Finally it should be
|
|
|
|
32
|
|
|
|
OUTPUT 5MHi
|
|
|
|
FREQUENCY SYNTHESIS
|
|
AMPLI 3KH2
|
|
FC
|
|
|
|
MOO. 30Hz,
|
|
®
|
|
|
|
CRYSTAL
|
|
|
|
OSCILL 5MHz
|
|
|
|
FC,
|
|
|
|
FREQUENCY MULTIPLIER
|
|
|
|
9 192
|
|
|
|
AMPLI 30Hz.
|
|
|
|
^1 -.T---I
|
|
L° {D--°'
|
|
|
|
MOD SKHz
|
|
|
|
GaAs LASER
|
|
|
|
(P PHASE DETECTION
|
|
|
|
FC FREQUENCY CONTROL
|
|
|
|
Figure 5. Overall experimental set-up for optically pumped cesium beam frequency standard.
|
|
|
|
the theoretical value:
|
|
|
|
_
|
|
|
|
/hz =_9 192 631 770.05 + 426.7fl^ ^
|
|
|
|
(7)
|
|
|
|
(H in gauss = 10 tesla),
|
|
|
|
with a regression coefficient = 0.99978.
|
|
|
|
5. Conclusions
|
|
|
|
Although these preliminary measurements are too coarse to establish claims of high accuracy regarding 2nd-order Doppler shift or cavity phase-shift, the results obtained, are encouraging and the experiments will be continued with improved electronics, especially concerning the stabilization of the laser frequency (which incidentally, could be used also, in the same apparatus, as a secondary length standard).
|
|
The potentiality of this frequency standard for accuracy of the order of 10"^'* will also depend on the absence of an eventual "light-shift" produced by stray laser light or fluorescence of the beam and precautions should be taken against this effect. Also, the need for liquid helium for the laser cryostat is a drawback for operation of the clock over a long period of time. However, laser diodes have already been developed for operation at room
|
|
temperature, with lifetimes in excess of several thousands of hours of operation, and this should allow the realization of more practical devices than the laboratory apparatus just described.
|
|
|
|
noted that the laser diode used could lase on the same frequency for slightly different conditions of current and temperature, corresponding to different modes of oscillation, and since some modes were less noisy than others,
|
|
the values of stability or precision quoted here may vary
|
|
slightly from one experiment to the other.
|
|
|
|
4.2 Experimental Results
|
|
|
|
Measurements of the locked oscillator frequency every
|
|
10 seconds, for a period of one hour, show that the distribution of the data is Gaussian (x^ = 3.6) with a standard deviation of about -S = 5 x 10"^^ and an Allan variance a^(lO) = 3 X 10-11.
|
|
|
|
As said previously, the short-term stability is better
|
|
|
|
3^4 with the laser frequency locked to the
|
|
|
|
than to the
|
|
|
|
3^3 transition. For example, in one experiment, with
|
|
|
|
the 3 -» 4 transition: S = 7.8 x lO'^^ and UyilO) - 3 x
|
|
|
|
10"" whereas with the 3 3 transition: S = 1.4 x 10"!°
|
|
|
|
and (Ty(lO) = 4.6 x
|
|
|
|
The precision resetability from an offset resonance frequency was on the average ±3 x lO'^^.
|
|
|
|
The effect of rf power variations on the precision of the clock depended very much on cavity tuning. For example, for a slight frequency detuning of the microwave cavity the frequency shift could be as large as 1.3 x 10"" for a 3 dB variation in rf power from optimum power. However,
|
|
with fine adjustment of the cavity tuning, this shift could
|
|
be made smaller than 2 x 10 ~ " and probably much smaller with improvements in the measuring equipment.
|
|
Variation of the laser light intensity was also studied
|
|
|
|
for possible frequency shifts due to the fluorescence of the cesium beam. Within the accuracy of the measuring equip-
|
|
ment (±2 x 10 ") no light-shift of the microwave resonance could be detected when the laser light was reduced by as much as 50 percent of its maximum intensity.
|
|
|
|
The absolute accuracy of the clock was observed by
|
|
H changing the static magnetic field in the microwave
|
|
cavity and measuring the corresponding frequency shifts. With a large number of observations, a least-squares fit
|
|
of the results gave the following relation, very close to
|
|
|
|
The author wishes to thank Professor A. Kastler, who
|
|
initiated the experiment, for his continuous encourage-
|
|
ment. The work was done in collaboration with Dr. J.-L. Picque of Laboratoire Aime Cotton, Orsay, and with the
|
|
helpful advice of S. Roizen. Appreciation is also expressed to Dr. T. Yabuzaki' and I. Hirano- for temporary help in the early phase of the work, and to G. Faucheron, D. Guitard, and P. Pages, for contributing technical help.
|
|
References
|
|
[I] D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, .Jr.,
|
|
Metrologia 1.3, 17 (1977). [2] H. Hellwig, S. Jarvis, D. Halford, and H. E. Bell, Metrolo-
|
|
gia 9, 107 (1975).
|
|
[3] A. Kastler, J. Phys. Radium 11, 155 (1950); J. Opt. Soc. Am. 47, 460 (1957).
|
|
[4] J. Brossel, B. Cagnac, and A. Kastler, J. Phys. Radium 15, 6
|
|
(1954).
|
|
[5] P. Cerez, M. Arditi, and A. Kastler, C. R. Acad. Sci. Ser. B: 267, 282 (1968).
|
|
M. Arditi and P. Cerez, IEEE Trans. Instrum. Meas. IM-21,
|
|
391 (1972).
|
|
P. Cerez and F. Hartmann, IEEE Trans. Quantum Electron.
|
|
QE-13, 344 (1977). [6] J.-L. Picque, Metrologia 13, 115 (1977). [7] M. Arditi and J.-L. Picque, C. R. Acad. Sci. Ser. B: 290, 461
|
|
(1980), also in English: J. Phys. (Paris) Lett. 41, L379
|
|
(1980).
|
|
[8] S. Jarvis, Jr., Metrologia 10, 87 (1974). [9] M. Arditi, I. Hirano, and P. Tougne, J. Phys. D. 11, 2465
|
|
(1978).
|
|
[10] E. Bernabeu, P. Tougne, and M. Ai-diti, C. R. Acad. Sci. Ser. B: 268, 321 (1969).
|
|
M. Arditi and P. Tougne, C. R. Acad. Sci. Ser. B: 280, 405
|
|
(1975);
|
|
Rev. Phys. Appl. 11, 665 (1976). [II] J.-L. Picque, S. Roizen, H. H. Stroke, and 0. Testard, Appl.
|
|
Phys. 6, 373 (1976).
|
|
^Ionosphere Research Laboratory, Kyoto, Japan -National Research Laboratory of Metrologj-, Ibai-aki, Japan
|
|
|
|
33
|
|
|
|
J.-L. Picque, and S. Roizen, Appl. Phys. Lett. 27, 340
|
|
(1975).
|
|
L. S. Cutler and L. Lewis, National Bureau of Standards,
|
|
Boulder, CO (private communication).
|
|
|
|
[13] N. F. Ramsey, Molecular Beams, (Oxford University Press, London, 1963), p. 129.
|
|
[14] P. Cerez, C. R. Acad. Sci. Ser. B: 272, 897 (1971).
|
|
|
|
34
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Frequency Measurement of Optical Radiation
|
|
K. M. Baird
|
|
National Research Council of Canada, Ottawa, Canada K1A 0R6
|
|
The feasibility of directly relating the frequency of visible radiation to microwave standards has been demonstrated and a number of frequency comparison systems linking infrared frequencies to the cesium primary standard have already been operated. These have yielded sufficient accuracy that together with wavelength measurement based on the ^^Kr line used to define the Meter, the standard of length can now be based without fear of a significant discontinuity, on a conventional value for the speed of light and the Cs standard for time. This paper reviews present and proposed frequency comparison chains and discusses their possibilities. Limitations for the general use of frequency comparison methods in the optical region are described.
|
|
Key words: frequency chains; laser frequency phase locking; optical frequency measurement; standard
|
|
of length.
|
|
|
|
1. Introduction
|
|
Among the remarkable facts of modern technology, I
|
|
think one of the most striking is that the possibility is at hand of making an exact count of events that occur at a rate of over 500 million in a microsecond. As you will hear in this and a later paper of this conference, the recent work leading to a redefinition of the Meter has involved the measurement of optical frequencies. Although the actual counting of optical frequencies or phase locking them to the cesium frequency standard has not yet been achieved, the feasibility of doing this has been
|
|
demonstrated and a number of laboratories are now en-
|
|
gaged in setting up equipment for its realization. Before discussing the techniques that are used to accomplish the remarkable feat mentioned above, let us look briefly at the basic principles used to measure a high frequency in terms of a lower one.
|
|
Figure 1 illustrates how a device that has a non-linear
|
|
response will convert a sinusoidal signal into an output that is distorted, i.e., it contains harmonics of the original signal. Depending on the response characteristic, the
|
|
output may contain harmonics of significant amplitude up
|
|
to very high orders (a hundred or more). Similarly, as shown in Fig. 2, such a device will convert a mixture of
|
|
3
|
|
3 O
|
|
|
|
INPUT
|
|
|
|
A Figure 1.
|
|
|
|
purely sinusoidal input is converted by a device
|
|
|
|
whose 7'esponse is 7ion-linear, as shoivn at the upper left, into a
|
|
|
|
distorted sinusoidal output, i.e., one that contains one or more
|
|
|
|
harmonics as shown in the lower right.
|
|
|
|
=)
|
|
o
|
|
|
|
INPUT
|
|
|
|
A Figure 2.
|
|
|
|
signal consisting of the superposition oj two
|
|
|
|
purely sinusoidal waves of slightly different frequencies is con-
|
|
|
|
verted by a device whose response is non-linear into an output
|
|
|
|
that contains a component whose frequency is equal to the
|
|
|
|
difference or beat between the original signals.
|
|
|
|
two sinusoidal signals of slightly different frequencies,
|
|
|
|
into a distorted output that contains a signal correspond-
|
|
|
|
ing to the difference frequency or beat between the two
|
|
|
|
A original signals.
|
|
|
|
count of the beats over a period of
|
|
|
|
time yields exactly the difference in the number of cycles
|
|
|
|
of the original signals. It can be seen that if two signals,
|
|
|
|
one of which is nearly equal to a harmonic of the other,
|
|
|
|
are impressed upon such a device having a suitable non-
|
|
|
|
linear response, the rather complicated output will con-
|
|
|
|
tain a low frequency signal of frequency equal to the
|
|
|
|
difference between the one and the harmonic of the
|
|
|
|
other. Thus a measurement of the frequency of the beat,
|
|
|
|
/b, will yield the value of the higher frequency /h in
|
|
terms of the lower /i, /h = Nfi + /b. The frequency of
|
|
the beat can be low enough to handle in convenient elec-
|
|
|
|
tric circuits and be measured or counted. The only re-
|
|
|
|
quirement for high speed is in the device for harmonic
|
|
|
|
generation and mixing. Of course the oscillations must be
|
|
|
|
sufficiently coherent (i.e., they must suffer frequency
|
|
|
|
changes sufficiently slowly) to allow observation of
|
|
|
|
enough beat oscillations to make a significant measure-
|
|
ment. When suitably applied, the method makes it possi-
|
|
|
|
ble to measure the number of oscillations of the higher
|
|
|
|
frequency signal during a given number of periods of the
|
|
|
|
lower, without missing one.
|
|
|
|
35
|
|
|
|
—
|
|
|
|
——
|
|
|
|
2. Techniques for Measurement of Optical Frequencies
|
|
|
|
Two major developments have made it possible to ap-
|
|
|
|
ply the above methods to extend frequency measurement to the optical region of the spectrum: the first was the in-
|
|
|
|
vention of the laser, which satisfied the coherence re-
|
|
|
|
quirement, and with the associated development of
|
|
|
|
Doppler-free spectroscopy and techniques for stabiliza-
|
|
|
|
tion, provided very precise reference standards; the
|
|
|
|
second was the development of very high speed non-
|
|
|
|
linear devices of which the most important for the
|
|
|
|
present discussion is the point contact metal-oxide-metal
|
|
|
|
(MOM) diode. It can be used for harmonic generation and
|
|
|
|
mixing to produce an electrical output from signals in the
|
|
|
|
range from dc to the infrared. Of nearly equal importance
|
|
|
|
was the production of optical non-linear crystals which
|
|
|
|
can be used to generate second harmonics and for the ad-
|
|
|
|
dition or subtraction of infrared and optical frequencies.
|
|
|
|
They require a detector for conversion into an electrical
|
|
|
|
signal.
|
|
|
|
MOM The development of the
|
|
|
|
diode was an extension
|
|
|
|
of the well known point contact technique (such as used
|
|
|
|
in old crystal radio receivers). This has been adapted to
|
|
|
|
achieve very high response speed by the use of small,
|
|
|
|
low resistance, low capacitance junctions that result
|
|
when the very fine tip (Fig. 3) of an etched tungsten
|
|
|
|
wire is brought into contact with an oxidized nickel post. The contact area can be of the order of 10"^^ cm^ so that
|
|
|
|
the very low capacitance and the high speed of the elec-
|
|
|
|
trical response, thought to be due to electron tunneling
|
|
through the 8-10 A nickel oxide layer, allows its use as an electrical device at frequencies up to about 200 THz (X = 1.5 |xm).
|
|
|
|
Figure 3. An electroyi photomicrograph of the etched tip of a
|
|
fine tungsten ivire showing the very small radius that can be 2ised to create junction diodes of extremely small area.
|
|
Overlapping this region, from about 30 THz (10 ixm) up
|
|
to frequencies of radiation in the visible and ultraviolet, non-linear optical crystals are used for harmonic generation and signal mixing, giving an output that with suitable sensitive detectors yields beat frequencies in the form of usable electrical signals. There are, however, limitations to the use of crystals: firstly, the crystals have limited ranges of transparency, and secondly, there is the problem of phase matching. This problem arises because the harmonic signal generated at a given place in the crystal is extremely small. In order to get usable signals, the contributions along a considerable length of path must add up in phase, i.e., the harmonic generated "downstream" must be in phase with the harmonic that has come from "upstream." Because of dispersion the
|
|
phase velocity of the generating beam and the harmonic
|
|
will normally differ and this adding up will not occur, but
|
|
|
|
it can often be effected by compensating for dispersion by making use of double refraction, a trick that requires precise adjustment of the indexes of refraction at the two frequencies, either by temperature or by the direction of propagation with respect to the crystal axes.
|
|
|
|
Although the above developments have opened up the
|
|
|
|
possibility of direct frequency comparison of optical with
|
|
|
|
microwave frequencies, its realization is far from simple
|
|
|
|
and a great deal remains to be done before the frequency
|
|
|
|
of visible radiation can be correlated directly with mi-
|
|
|
|
crowave standards. Problems arise from the fact that the
|
|
|
|
frequencies involved are so very high, so that even very
|
|
|
|
small relative differences result in beat frequencies that
|
|
|
|
are high compared to those that can be handled in con-
|
|
|
|
venient state-of-the-art circuitry. This makes trouble in
|
|
|
|
two ways: small frequency instabilities in the lasers
|
|
|
|
cause very large excursions in the beat . . . e.g., a jitter
|
|
|
|
J of 10-
|
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|
at
|
|
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|
100 THz (\
|
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|
=
|
|
|
|
3
|
|
|
|
m) ^JL
|
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|
|
is
|
|
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|
100 MHz,
|
|
|
|
and if the
|
|
|
|
sought for beat signal is of this order, measurement be-
|
|
|
|
comes very difficult to say the least. Secondly, matching
|
|
|
|
the harmonic of one source to the frequency of another
|
|
|
|
source to produce low frequency beats is not easy be-
|
|
|
|
cause of the limited choice of reference lasers and of
|
|
|
|
their limited tuning range. This situation is illustrated in
|
|
|
|
Fig. 4; the top half shows on a log scale the five decades
|
|
in frequency from the cesium standard at 9 GHz to the
|
|
|
|
visible. The ranges of klystrons and the range of opera-
|
|
|
|
MOM tion of the W-Ni
|
|
|
|
diode are indicated, as well as im-
|
|
|
|
portant bench mark frequencies of Cs, UCN, H2O, CO2,
|
|
|
|
etc., up to the L lines on which HeNe and argon lasers
|
|
|
|
can be stabilized. Since our frequency comparison
|
|
|
|
method depends to a considerable extent on the simple
|
|
|
|
addition of frequencies, particularly at the higher ranges
|
|
|
|
and since it yields output signals that correspond to
|
|
|
|
differences, the difficulties are more appropriately illus-
|
|
|
|
trated by the use of a linear scale, as done in the bottom
|
|
|
|
half of the figure. On this scale the total range of fre-
|
|
|
|
quency comparison and measurement from sub-kHz
|
|
through the GHz microwave bands that have been made
|
|
|
|
possible with commercial equipment development and by
|
|
|
|
the pioneering experiments in the infrared done in the
|
|
sixties at MIT covers only a very small part at the left of
|
|
|
|
the scale. The enormous range yet to be covered to reach
|
|
|
|
the visible as well as the large size of the gaps between
|
|
|
|
available bench mark lasers is evident. This can be em-
|
|
|
|
phasized further by considering an appHcation of the rich
|
|
m 10 |JL bands of CO2 laser lines indicated on the figure.
|
|
|
|
'''III, LOG FREQUENCY (Hz)
|
|
|
|
9
|
|
|
|
'0
|
|
|
|
II
|
|
|
|
12
|
|
|
|
13
|
|
|
|
14
|
|
|
|
15
|
|
|
|
Cs
|
|
^
|
|
KLYSTRONS
|
|
|
|
HCN
|
|
\
|
|
W-Ni DIODE
|
|
|
|
HjO COg CH^ Ne
|
|
|
|
\
|
|
|
|
1 H-ii\
|
|
|
|
VISIBLE
|
|
|
|
FREQUENCY (THz)
|
|
|
|
1
|
|
|
|
1-9
|
|
1
|
|
|
|
\
|
|
3.39
|
|
|
|
W-Ni DIODE
|
|
|
|
200
|
|
|
|
300
|
|
|
|
400
|
|
|
|
1 1
|
|
|
|
— Ne Ne
|
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|
|
1
|
|
|
|
1
|
|
|
|
1.52
|
|
|
|
1.15
|
|
|
|
X (^m)
|
|
|
|
500
|
|
1
|
|
|
|
600
|
|
1
|
|
|
|
H\
|
|
.633.612.576
|
|
|
|
\
|
|
.515
|
|
|
|
VISIBLE
|
|
|
|
Figure 4. The spectrum covered by optical frequency measurement on a log scale (top) and a linear scale (bottom) of frequeyicy showing the important "bench mark" lines.
|
|
|
|
36
|
|
|
|
One of these bands is shown in enlarged detail in Fig. 5. These very conveniently produced lines are spaced about
|
|
40 GHz apart covering a range of about two terahertz
|
|
and a number of such bands can be produced using various isotopes. However the gap between the lines is usually more than 100 times the gain width (i.e., tuning range) of the lines; in other words the band is more than 99% empty space. Thus, for example it might be thought
|
|
straightforward to measure a CO laser line (at about
|
|
5 (xm) by comparison with the second harmonic of one of the CO2 lines; in fact the chance of finding a coincidence
|
|
closer than several GHz is very slight. In such a case the
|
|
gap usually has to be covered by the addition of a klystron generated frequency as will be seen in several exam-
|
|
ples below.
|
|
|
|
27.5
|
|
|
|
Frequency (THz)
|
|
|
|
28.0
|
|
|
|
28.5
|
|
|
|
29.0
|
|
|
|
29.5
|
|
|
|
Figure 5. The 10 [xm band of the CO, laser.
|
|
The CO2 band shown and similar overlapping bands produced by the use of CO2 sequence hnes and CO-, of dif-
|
|
ferent isotopic composition provide a very important set
|
|
having frequencies very accurately known relative to one
|
|
another and covering the range from about 26 to 33 THz
|
|
(9 to 11 |ji,m). These radiations and their harmonics as well as radiations generated by the sums and differences of pairs, and harmonics of the differences, can be added to and subtracted from other laser radiations by the use
|
|
of W-Ni diodes up to about 1.5 ixm; above this point the diodes appear not to respond electrically. The CO2 laser
|
|
is thus of great importance in frequency comparison
|
|
chains. In certain cases CO2 laser frequencies can be added to radiations above this limit, thus making it possible in effect to transfer the band of frequencies to another
|
|
region of the spectrum, (e.g., at 0.633 (xm) by the use of
|
|
non-linear crystals. However the requirement that the
|
|
crystal be transparent to all radiations involved, the requirement of phase matching, and the very small non-
|
|
hnear coefficients very much limit the possibilities, as will
|
|
be seen.
|
|
Referring again to Fig. 4 the scarcity of bench mark laser lines can be somewhat alleviated by the use of tunable dye lasers in the visible, and, recently, of color center lasers in the range from —2.5 [xm to 1 \xm as will
|
|
be discussed later.
|
|
From the foregoing discussion it is evident that,
|
|
despite the simplicity of the basic principle, extension to the optical region of frequency comparison with respect to microwave standards is far from easy. Nevertheless
|
|
the first measurement of a visible frequency has already been demonstrated [1], and several measurements of infrared frequencies have been made with very high accuracy [2-4]. Taken in conjunction with wavelength
|
|
|
|
measurement with respect to the **Kr length standard, they make possible a new definition of the Meter based on the standard of time and the adoption of a conventional value for the speed of light; this will be discussed in another paper at this conference.
|
|
|
|
3. Chains to Compare Infrared and Microwave Frequencies
|
|
|
|
The frequency chains to the infrared will be described
|
|
|
|
with reference to Fig. 6 where they are shown, greatly
|
|
|
|
simplified, in roughly the chronological order in which
|
|
|
|
they were successfully operated (or are expected to
|
|
|
|
operate). The first measurement of the frequency of a
|
|
CH4 stabihzed He-Ne laser was made at NBS (Boulder)
|
|
|
|
by Evenson and his colleagues [5]. Following up the
|
|
pioneering work at MIT on W-Ni diodes in the far in-
|
|
|
|
frared, they gradually extended the chain, and succeeded
|
|
|
|
in measuring the CHj line at 88 THz (3.39 ixm), in 1972.
|
|
Almost simultaneously the group at NPL in London set
|
|
|
|
up a very similar chain [6] and obtained results in very
|
|
|
|
good agreement with NBS. In these chains as shown, the
|
|
|
|
output of a klystron of frequency 74 GHz, was compared
|
|
|
|
HCN with an
|
|
|
|
laser by generation of the 12^^ harmonic
|
|
|
|
and mixing in a conventional tungsten silicon microwave
|
|
|
|
HCN diode. The
|
|
|
|
laser output was in turn compared to
|
|
|
|
the H2O laser line at about 10 THz by generation of its
|
|
|
|
12'*' harmonic and mixing in a W-Ni diode. The H2O line
|
|
|
|
was multiplied by three and compared with CO2 laser ra-
|
|
|
|
diation at 30 THz, again in a W-Ni diode, and finally, the 30 THz radiation was multiplied by three and compared
|
|
|
|
with a CH4 stabilized HeNe laser at 88 THz. As men-
|
|
|
|
tioned, this description is very much simplified: for exam-
|
|
|
|
ple, at nearly all stages above the first klystron stage,
|
|
|
|
additional klystron frequencies had to be added or sub-
|
|
|
|
tracted to reduce the output beat signal frequency to the
|
|
MHz range so as to be convenient for measuring; also the
|
|
|
|
fjiVi-lR Frequency Chains
|
|
|
|
0.1 T
|
|
NBS\ NPLi
|
|
|
|
I
|
|
—I—
|
|
HCN
|
|
|
|
10
|
|
|
|
100 THz
|
|
|
|
WW
|
|
|
|
3~
|
|
|
|
'3
|
|
|
|
'
|
|
|
|
H,0
|
|
|
|
NRC
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
I
|
|
|
|
NPL IS
|
|
|
|
W-Si
|
|
|
|
w
|
|
|
|
Ale
|
|
|
|
W,
|
|
|
|
W
|
|
|
|
HCN ^ D2O
|
|
|
|
LPTF -+- W-Si
|
|
Kl
|
|
|
|
W I I
|
|
|
|
NRLM
|
|
|
|
+4h
|
|
|
|
PTB
|
|
|
|
W-Si
|
|
|
|
W-GaAs
|
|
Care
|
|
|
|
NBS NBS
|
|
|
|
Ale Optical Synchrotron
|
|
|
|
C.C.
|
|
^?
|
|
|
|
Figure 6. Simplified schematic diagram of frequency compari-
|
|
|
|
son chains at the National Laboratories indicated on the left,
|
|
|
|
covering the range from the microivave region to the 3 \im
|
|
|
|
wavelength region, the numbers indicate the harmonics used,
|
|
|
|
W W Kl = klystron;
|
|
|
|
= tungsten-nickel point contact diode;
|
|
|
|
-
|
|
|
|
Si = tungsten-silicon diode, etc.; A = difference frequency gen-
|
|
|
|
erated by two CO2 lasers.
|
|
|
|
37
|
|
|
|
CO2 line used for comparison to the H2O line was not the same line that was used in the comparison with CH4 and the difference had to be measured against a klystron fre-
|
|
quency. At NPL a different pair of CO2 hues was used in
|
|
this stage. These early experiments suffered loss of accuracy in the transfer from one stage to the next but in more refined repetitions of the experiments produced
|
|
frequency values for the CH4 and CO2 lines of accuracy approaching better than 10"^. It was these values that, taken together with wavelength measurements at NBS, NPL, and several other national laboratories, led to the
|
|
acceptance of 299792458 m/s as the best value for the
|
|
|
|
speed of light [7].
|
|
More recently, at NEC (Ottawa) [8] and at IS (Moscow)
|
|
[2] the frequency chains shown were put into operation.
|
|
At NRC the HCN and H2O laser stages were replaced by
|
|
the use of difference frequencies generated in W-Ni
|
|
diodes by simultaneous input from two CO2 lasers operat-
|
|
ing on appropriately chosen transitions. A considerable
|
|
|
|
advantage in the simplicity of the lasers is partially offset by the low signal strengths of the difference frequencies. This required the addition of an extra stage to reduce the harmonic numbers to 3, 3, and 4. The accu-
|
|
racy of the first measurement at NRC was limited by the
|
|
fact that each stage was measured separately, depending on saturated fluorescence stabilization of the CO2 lasers
|
|
for the transfer accuracy. This defect is being corrected
|
|
by the use of phase-locking in a new system now being set up; phase-locking of the beat frequency of two lasers, operating on lines of different CO2 isotopes, to a rubidium standard has already been performed successfully. At IS, a D2O laser and harmonic factors of 8 and 3 were used instead of the H2O laser and factors of 12 and 3 used at NBS; an OSO4 stabilized CO2 laser was used as the 30 THz transfer.
|
|
In a recent revised version of the NPL chain [3] the
|
|
number of stages was reduced as shown by the use of 43"' harmonic generation in a Josephson junction to go from the klystron stage to a CO2 pumped alcohol laser at 4.25 THz; from there two stages of 7x and 3x were used to go via a
|
|
CO2 laser to the CH4 stabilized HeNe laser at 3.39 [xm. In
|
|
this measurement the stages were operated simultaneously and phase locking or continuous beat frequency counting was used at all points to give a much higher accuracy (3 X 10"^^) than in the previous experiment.
|
|
|
|
The last chain that, to date, has been reported as hav-
|
|
ing operated is that at LPTF (Paris) [4]. It makes use of
|
|
HCN and an alcohol laser in the lower stages. The NRLM (Tokyo) chain, which is to be described at this
|
|
conference, makes use of alcohol and HoO lasers to reach
|
|
the CO2 lines at 30 THz. The PTE (Braunschweig) chain
|
|
|
|
is in the stage that all the parts are operational but final
|
|
stabilization and locking to make a measurement of the CH4 line has yet to be done.
|
|
|
|
The newest NBS chain, shown near the bottom of
|
|
|
|
Fig. 5, is part of a continuous system designed to go to the visible. It will use harmonic numbers of 7, 7, 7, and 5 to go from the klystron region, via alcohol and CO2 lasers, to a color center laser at 2.52 [xm (130 THz); more wiW be said later about the upper stages to the visible.
|
|
|
|
The last system shown in the figure, also being set up
|
|
|
|
NBS at
|
|
|
|
(Boulder), is quite different from all the others
|
|
|
|
and is intended to go directly from the rf region to at
|
|
|
|
least the infrared by using the principle of the synchro-
|
|
|
|
tron. An electron orbiting in synchronism with an rf field
|
|
|
|
will pass through a focussed laser beam in such a manner
|
|
|
|
that, if the orbital period, i.e., the rf, is an exact sub-
|
|
|
|
multiple of the laser frequency, the electron will get a
|
|
|
|
'
|
|
' kick' '
|
|
|
|
from the
|
|
|
|
electric field of the laser on each revolu-
|
|
|
|
tion and a resonance will be observed. The method has an advantage, in addition to that of having only one stage, in that it is a frequency division, rather than frequency multiplication method, and as such will not suffer from the problem of phase jitter amplification.
|
|
Before proceeding to a description of techniques to extend frequency measurements into the visible, it is appropriate to consider the accuracy demonstrated in meas-
|
|
urements of the CH4 line frequency reported up to the
|
|
present. Figure 7 shows the latest values reported by each laboratory with standard deviation error bars. It is
|
|
seen that these agree to within one in 10'', i.e., well within the precision of the present meter definition. There is only one case (IS) where the error bars do not overlap.^ The uncertainties are still far from the limit imposed in principle by proper frequency comparison with
|
|
the Cs standard (lO'^^) but the NPL value (3 x lO'^^) is
|
|
within the uncertainty known to be attributable to lack of reproducibility of the CH4 lasers as used. Evidence for this uncertainty comes from two international direct comparisons of CH4 lasers, one amongst NPL, PTB, and
|
|
BIPM [9] and the other between BIPM and VNIIFTRI
|
|
(Moscow) [10].
|
|
|
|
F = 88 376 181 000 kHz +
|
|
|
|
400
|
|
|
|
500
|
|
|
|
600
|
|
|
|
700
|
|
|
|
800
|
|
|
|
.
|
|
|
|
NBS
|
|
|
|
•
|
|
|
|
I
|
|
|
|
1
|
|
|
|
NPL
|
|
|
|
'
|
|
|
|
I
|
|
|
|
1
|
|
|
|
1--O--1
|
|
NRC
|
|
|
|
IS NPL LPTF
|
|
|
|
^ H.H
|
|
9
|
|
|
|
Figure 7. Results obtained at various laboratories for the frequency of the He-Ne laser line at 3.39 p^m stabilized to the P(7) absorption line in methane.
|
|
4. Extension of Frequency Measurement to
|
|
the Visible
|
|
Systems designed to extend direct frequency comparison to the visible part of the spectrum are shown in very simplified schematic form in Fig. 8. Only the first of
|
|
these, the NBS-NRC chain [11, 1], has been demon-
|
|
strated to completion, yielding a frequency for an I2 absorption line in the visilDle. The ISP (Novosibirsk) system has been demonstrated to function but the component frequencies have not been measured [12]. The other
|
|
three systems are under active development and many parts of them are already operational.
|
|
In the NBS-NRC experiments the frequency of a Xe laser at 150 THz (2.02 |xm) was first measured by com-
|
|
parison in a W-Ni diode with the sum frequency of a HeNe laser at 3.39 fxm (88 THz) and two 10 |xm CO2 lines
|
|
Recent measurements have revised the IS value upwards by 17.4 kHz
|
|
[20].
|
|
|
|
38
|
|
|
|
IR-Visible Frequency Chains
|
|
|
|
0
|
|
|
|
100
|
|
|
|
200
|
|
|
|
300
|
|
|
|
400
|
|
|
|
500 THz
|
|
|
|
Figure 8. Simplified schematics of frequency comparison
|
|
|
|
chains at the National Laboratories indicated on the left cover-
|
|
|
|
ing the range from 10
|
|
|
|
waveleyigth (30 THz) to the visible
|
|
|
|
X (600 THz). C = CO., laser; CC = color center laser; = Xe
|
|
|
|
N laser; = He-Ne or pure Ne laser; LN = frequency generated
|
|
|
|
in a LiNbO^ crystal.
|
|
|
|
(-30 THz). The sum of the Xe Une and a CO Une at 50 THz was used to measure the 1.5 |xm (196 THz) HeNe laser line, again in a W-Ni diode. In the final part of
|
|
the experiment done at NBS, the He-Ne 1.5 (xm Hne was added in a proustite crystal to the sum of two COo lines (produced by addition in a CdGeAs crystal) resulting in a
|
|
sum frequency very near 1.15 jjim. A pure Ne 1.15 jjtm
|
|
(260 THz) laser output was compared by the use of a
|
|
Schottky diode. The Ne laser, stabilized on its Lamb dip,
|
|
was taken to NRC and compared to a 1.15 |xm He-Ne
|
|
laser whose radiation, after doubling, was locked to an I2 line by saturated absorption. This experiment, done in 1979, thus demonstrated for the first time the direct measurement of a frequency in the visible. It ought to be
|
|
mentioned however that the CO frequency was not
|
|
directly measured but was inferred from molecular con-
|
|
stants based on frequency measurements. In fact, to
|
|
date, the best knowledge of the 520 THz frequency is derived from its measured wavelength. The weak CO link
|
|
could be corrected, but present efforts are directed to what appear to be more attractive systems as described
|
|
below.
|
|
In the ISP system three Ne transitions at 3.39, 2.39, and 1.15 ixm were excited simultaneously in a He-Ne
|
|
plasma; non-Hnear interaction in the plasma itself pro-
|
|
duced a sum frequency at 0.633 |xm (474 THz). Although very elegant in principle the scheme has not been widely adopted because of apparent difficulties in measurement and control of the component frequencies.
|
|
The third chain shown, under development at NBS
|
|
(Boulder), starts with a CO2 Hne (shown at the end of their chain in Fig. 6) whose fifth harmonic generated in a W-Ni diode is used to control the frequency of a color center laser at 130 THz. The frequency of the color center laser is doubled to 260 THz in a LiNbOs crystal,
|
|
|
|
and used to control a He-Ne 1.15
|
|
|
|
laser. The fre-
|
|
|
|
quency of the latter is doubled in a second LiNbO^ cry.s-
|
|
|
|
tal for reference to the I2 line at 520 THz as in the NBS-
|
|
NRC experiment. An additional stage has been proposed
|
|
|
|
that would use the difference frequency of the 520 THz
|
|
|
|
line and a carbon monoxide laser line to measure the
|
|
|
|
widely used He-Ne, I2 stabilized 0.633 \xm line. However
|
|
|
|
a suitable crystal was not identified.
|
|
|
|
The fourth system shown in the figure, being
|
|
developed at NRC, makes use of two Xe laser Hnes ex-
|
|
cited simultaneously in the same laser and measured by reference to CO2 laser lines in W-Ni diodes. The Xe lines are added in LiNbOs and compared with the difference frequency generated by mixing a 1.15 |xm He-Ne laser and a CO2 line in a proustite crystal, thus giving the frequency of the He-Ne line. The latter can be compared
|
|
with the I2 line at 520 THz as described above. Some dif-
|
|
ficulties in this system are associated with the proustite difference frequency generation and low S/N but the problem could be very much alleviated by the use of a AgGaS2 crystal, expected to be available in the near
|
|
|
|
future.
|
|
|
|
The last system shown, nearing completion at NPL, is
|
|
similar to the NBS system in the use of a color center
|
|
laser whose frequency is doubled in a LiNbOs crystal but will make use of parametric conversion in LiNbOs to detect the difference between an I2 stabilized He-Ne
|
|
laser (0.633 jjim) and four times the frequency of the
|
|
color center laser. Also it uses only the fourth harmonic of a different starting CO2 line and a lower frequency
|
|
color center laser, than in the NBS case, to reach the
|
|
lower frequency (474 THz) visible line.
|
|
|
|
In concluding this description of the schemes for reaching visible frequencies it is emphasized that, as in the case of the infrared frequency measurement, the experi-
|
|
ments are much more complex than one might judge. This can be illustrated by describing in more detail the apparently simple stage of stabilizing doubled Ne
|
|
|
|
1.15 |jLm radiation with reference to an lo line as used in
|
|
the NRC-NBS experiment. This elegant experiment, performed by Hanes at NRC
|
|
[13] is shown schematically in Fig. 9. It employs a double
|
|
resonant cavity seen at ABCBE and EBFG. The 1.15 ixm
|
|
radiation produced by the He-Ne plasma tube is focussed into the LiNbOa crystal which is accurately temperature controlled for phase matching so as to produce doubled frequency at 520 THz (0.576 |xm). An additional phase matching requirement is satisfied by a special dispersive reflector at E to ensure that the reflected second har-
|
|
monic is in phase with the second harmonic generated
|
|
from the reflected fundamental radiation (1.15 iJim). An
|
|
|
|
Figure 9. Schematic diagram of apparatus for stabilization of
|
|
|
|
doubled He-Ne 1.15 fjL>?z laser on an
|
|
|
|
line at 576 nm
|
|
|
|
(520 THz).
|
|
|
|
39
|
|
|
|
I2 cell in the second cavity, resonant at the doubled frequency, produces saturated absorption features that can be used for stabilization. Scanning and servo control of
|
|
the cavity arms AC, CE, and EG are suitably coordi-
|
|
nated so as to be resonant simultaneously at the required frequencies. About 100 |jlW of 1.15 \xm radiation is emit-
|
|
A ted at and about 20 |jlW of 0.576 |xm radiation at G.
|
|
The fortunate I2 hyperfine spectrum at 520 THz is shown
|
|
in Fig. 10. Note the strong component at the left where the gain has been reduced by a factor of 10.
|
|
At present it looks as if the optical frequency measurement systems described above stand an excellent chance
|
|
of working and could, at least in principle, result in phase correlation of visible laser radiation with the standard Cs frequency. This might be done by a completely phase locked system or by a simultaneous count of beats at some of the stages. In any case the frequency of good reference lines in the visible will be measured,
|
|
but they may amount to only a few bench marks at
|
|
0.576 |xm, 0.633 ixm, probably at 0.612 jjim, and possibly
|
|
an I2 line near the Ha line at 0.656 fxm. Let us next consider the problems and some methods for establishing and of making use of such bench marks for measurement
|
|
of other lines in the visible and infrared.
|
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|
|
200
|
|
|
|
400
|
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|
|
600
|
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|
|
800
|
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|
|
FREQUENCY CMHz)
|
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|
|
o
|
|
|
|
nm 1 k J I hg
|
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|
|
f
|
|
|
|
edcb
|
|
|
|
a
|
|
|
|
Figure 10. I , Hyperfine spectrum at 520 THz obtained with the
|
|
apparatus of Fig. 9.
|
|
|
|
5. The Use of Optical Frequency Standards
|
|
|
|
Once a bench mark is established in a given part of the
|
|
|
|
spedtrum, either in the form of a precisely reproducible
|
|
|
|
absorption line or a laser locked to a frequency chain, other lines or bench marks can be measured by the use of
|
|
methods like those described; this may require one or a number of steps. The process has become relatively
|
|
|
|
straightforward in the region covered by the point con-
|
|
|
|
MOM tact
|
|
|
|
diodes, i.e., up to about 1.5 |xm (200 THz).
|
|
|
|
Differences of up to a few tens of GHz can be measured
|
|
|
|
directly in the diode output; for greater separations, up to about 100 GHz, klystron radiation can be mixed to measure the differences. For yet greater separations, up to about seven terahertz, two CO2 lasers having the appropriate difference in frequency can be used; and finally, CO2 or other appropriate laser emission can be used to measure separations upwards of 25 THz.
|
|
|
|
One example of such a process is the work of Clairon et al. [14], who have established a grid of very precise
|
|
standards, separated by about 50 GHz, covering a range
|
|
of 265 GHz in the 10 ixm region. This was done by step-
|
|
|
|
ping off from a well measured OSO4 standard [2] by the use of a klystron, to OSO4 and SFe absorption lines that coincide with CO2 laser lines. Saturated absorption in the very narrow OSO4 and SFe lines made possible such precise setting (±1 kHz and ±3 kHz respectively) that they
|
|
contributed practically no significant error, even allowing for accumulation in a number of steps. Another example
|
|
of technique is the method used by Siemsen at NRC [15]
|
|
to measure the frequency of a laser that is well outside a grid of reference lines. As shown in Fig. 11, when two
|
|
appropriate known frequencies / 1 and / 2 are mixed with the unknown frequency / 3, the latter can be deduced from the beat frequency / b = (/i - f 2) - if 2 - f z)-
|
|
|
|
(f2- fa)
|
|
|
|
beat frequency
|
|
|
|
— —^ fa lOOmW — — =^ ^ f3 > 10mW
|
|
|
|
^ -80dBm
|
|
/
|
|
|
|
-40dBm
|
|
|
|
Volt Watt
|
|
|
|
Figure 11. The use of three wave mixing to measure the frequency of a laser line that lies outside a grid of known lines.
|
|
|
|
The measurement of large frequency differences gets
|
|
|
|
considerably more difficult above the electrical response
|
|
|
|
MOM limit of the
|
|
|
|
diodes (—1.5 iJirn). Photo electric detec-
|
|
|
|
tors can be used as square law devices to measure
|
|
directly differences up to several GHz in the region from
|
|
|
|
3 |jLm through the visible. Schottky diodes have also been
|
|
used to measure differences up to 122 GHz [16] by mixing
|
|
|
|
with klystron generated frequencies. In order to measure
|
|
|
|
greater differences or to generate harmonics, non-linear
|
|
|
|
crystals must be used.
|
|
|
|
The use of non-linear crystals for frequency comparison
|
|
|
|
involves far more restrictions than does the application of
|
|
MOM diodes because of their limited range of transpar-
|
|
|
|
ency, the problems of phase matching, and the small
|
|
|
|
non-linear coefficients; they cannot be used to mix klys-
|
|
|
|
We tron frequencies.
|
|
|
|
have seen examples of their appli-
|
|
|
|
cation in the frequency chains described but these tend
|
|
|
|
to be special cases and general applicability cannot be as-
|
|
|
|
sumed. For example AgGaS^ is a rather remarkable crys-
|
|
|
|
tal that is transparent from 13 (xm to well into the visible
|
|
|
|
and has a good conversion efficiency: one would expect it
|
|
to be ideal for the last stage in the NBS chain going from
|
|
|
|
520 THz to the 0.633 laser line. Unfortunately however,
|
|
|
|
according to published data [17], it is not possible to real-
|
|
|
|
ize phase matching for this case. The number of "special
|
|
|
|
cases," with the right transparency, phase matching,
|
|
|
|
and suitable laser lines may well become quite large,
|
|
|
|
however, with the further development of crystals and
|
|
|
|
tunable dye and color center lasers. There are cases al-
|
|
|
|
ready where one can, in effect, transfer the 7 THz-wide
|
|
|
|
grid of COo laser frequencies into part of the visible spec-
|
|
|
|
trum by mixing in proustite, and perhaps it is not unrea-
|
|
|
|
sonable to hope that more possibilities like this will turn
|
|
|
|
up.
|
|
|
|
Special tricks can be used to increase the measurement separation limit beyond that imposed by the photo electric detector. One such is that suggested by Hansch and
|
|
Wong [18] whereby a widely tunable laser is frequency
|
|
modulated so as to match the side band separation to the
|
|
|
|
40
|
|
|
|
intermode spacing; a comb of frequencies covering about 0.5 THz in the visible may be generated and locked to an absorption reference by two-photon absorption. Another example is the stepping procedure proposed by Meisel and his colleagues [19]. Using two stabilized dye lasers,
|
|
they plan to make two hundred steps of 80 GHz each in
|
|
order to measure the He, line with respect to the 0.633 I2
|
|
laser line.
|
|
6. Conclusion
|
|
It is clear fi'om the foregoing review that, although the direct measurement of frequencies in the optical region is
|
|
now possible, it still often involves the use of individual
|
|
ingenious and difficult experiments, particularly in the visible spectrum. For some time to come the best means for interpolation or extrapolation with respect to the few very accurate bench marks will be by the use of wavelength interferometry; certainly it is the most con-
|
|
venient for accuracies of 10"*^ or less. On the other hand
|
|
perhaps it is not an unreasonable hope that development
|
|
of new devices, such as possibly a broad band non-linear reflector, will make possible "day-to-day" use in the op-
|
|
tical region of the great accuracy and convenience inherent in the methods of frequency comparison.
|
|
The author acknowledges with thanks the help of his colleagues and especially the major contribution of G. R. Hanes to the preparation of this paper.
|
|
|
|
References
|
|
[1] K. M. Baird, K. M. Evenson, G. R. Hanes, D. A. Jennings, and F. R. Petersen, Opt. Lett. 4, 263 (1979).
|
|
[2] Y. S. Domnin, N. B. Koshelyaevskii, V. M. Tatarenkov, and
|
|
S. Shumyatskii, Pis' ma Zh. Eksp. Teor. Fiz. 30, 273 (1979) [JETP Lett. 30, 253 (1979)].
|
|
[3] D. J. E. Knight, G. J. Edwards, P. R. Pearce, and N. R. Cross, Nature 285, 388 (1980).
|
|
[4] A. Clairon, B. Dahmani, and .J. Rutman, IEEE Trans. In-
|
|
strum. Meas. IM-29, 268 (1980). [5] K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Daniel-
|
|
son, and G. W. Day, Appl. Phys. Lett. 22, 192 (1972). [6] C. C. Bradley, G. Edwards, and D. J. E. Knight, Radio
|
|
Electron. Eng. 42, 321 (1972). [7] Comptes Rendus des Seances de la Conf. Gen. des Poids et
|
|
Mesures, 15th, 103 (1975).
|
|
[8] B. G. Whitford, Opt. Commun. 31, 363 (1979). [9] B. W. Jolliffe, G. Ki-amer, and J.-M. Chartier, IEEE Trans.
|
|
Instrum. Meas. IM-25, 447 (1976). [10] N. B. Koshelyaevskii, A. Obukhov, V. M. Tatarenkov, A. N.
|
|
Titov, J.-M. Chartier, and R. Felder, Metrologia 17, 3
|
|
(1981).
|
|
[11] D. A. Jennings, F. R. Petersen, and K. M. Evensen, Appl. Phys. Lett. 26, 510 (1975); Opt. Lett. 4, 129 (1979).
|
|
[12] V. P. Chebotayev, V. M. Klementyev, and Y. A. Matyugin, Appl. Phys. 11, 163 (1976).
|
|
[13] G. R. Hanes, Appl. Opt. 18, 3970 (1979). [14] A. Clairon, A. VanLerberghe, C. Salomon, M. Ouhayoun,
|
|
and C. J. Borde, Opt. Commun. .35, 368 (1980).
|
|
[15] K. J. Siemsen, Opt. Lett. 6, 114 (1981). [16] H. -U. Daniel, M. Steiner, and H. Walther, Appl. Phys. 25,
|
|
7 (1981).
|
|
[17] G. D. Boyd, H. Kasper, and J. H. McFee, IEEE J. Quantum
|
|
Electron. QE-7, 563 (1971).
|
|
[18] T. W. Hansch and N. C. Wong, Metrologia 16, 101 (1980). [19] B. Bukhard, H. J. Hoeffgen, G. Meisel, W. Reinert, and B.
|
|
Vowinkel, these proceedings.
|
|
[201 U.S.S.R. State Committee of Standards Bulletin 16, Domnin, ei al., (1981) [ISSN 0135-2415].
|
|
|
|
41
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Optical Frequency Standards: Progress and Applications
|
|
J. L. Hall
|
|
Joint Institute for Laboratory Astrophysics, National Bureau of Standards and University of Colorado,
|
|
Boulder, CO 80309
|
|
The decade since the First International Conference on Precision Measurement and Fundamental Constants has witnessed dramatic progress in stable laser technology. For example, frequency stability [1], linewidth [2], and reproducibility [3] of ~3 x 10"''* have been reported for the methane-stabilized
|
|
HeNe laser at 3.39 |xm. Impressive performance has also been obtained wdth CO2 lasers stabilized with CO2 [4] and other molecular resonances [5]. In the visible, argon ion lasers with an I2 molecular
|
|
reference have given 10"'^ reproducibility [6]. Recently, a frequency reproducibility of 6 x 10"'^ has
|
|
been reported for the orange HeNe laser (612 nm) stabilized to an external I2 cell [7]. HeNe lasers
|
|
operating on the usual red line can give reproducibility in the 10"'' domain using intracavity absorp-
|
|
tion in I2 [8].
|
|
H However, to reach spectral transitions of particular physical interest (e.g., [9]) or of special prom-
|
|
ise as standards (e.g., Ca at 657 nm [10]) in general will require use of a broadly tuneable laser, typi-
|
|
— — cally using color center crystals or a flovdng dye solution as the active medium. Comparable stabiliza-
|
|
tion results with such tuneable lasers especially dye lasers is vastly more difficult than with gas
|
|
A lasers, although kilohertz linevndth dye lasers have just been reported [11]. technique suggested by
|
|
Drever [12] recently allowed achievement of sub-100 Hz dye laser linewidth [13]. High resolution optical interaction techniques based on Ramsey's method of "separated oscillating
|
|
fields" have been studied theoretically [14] and demonstrated experimentally using two-photon [15]
|
|
and/or multizone saturated absorption techniques [16] in atomic beams. As in the high resolution methane cell work [17], uncertainty in the second order Doppler shift provides the principal limitation to the accuracy of optical frequency standards [18], even using atomic beam/Ramsey resonance techniques [19]. Measurement of atomic beam velocity distributions may be accomplished with gated excitation of the Ramsey zones, analogous to the techniques employed vdth cesium microwave standards [20]. Alternatively, the interacting molecular beam velocity may be precisely defined with dual frequency, longitudinal saturation spectroscopy [21]. Useful signal/noise ratios may be feasible using sensitive cryogenic bolometeric detection of the excited beam [22] or using the recently-introduced optical heterodyne technique [23, 13] which appears to approach closely the fundamental quantum detection limit
|
|
[24].
|
|
The ultimate solution to the Doppler shift problem is surely to slow [25] and /or deflect [26] the atomic beam or to cool [27] electromagnetically-trapped ions using radiative processes. The only meaningful limitation to the latter technique may be inferred from the following: we provide an expanded list of interesting candidate transitions for atomic beam frequency standard investigations; however there are only three entries in a comparable list of suitable ions, filtered for compatibility with existing
|
|
potentially-stable laser sources.
|
|
— Although the ultrastable laser technology is still immature and of imperfect reliability especially — for cw dye lasers there is a certain temptation to begin applying these optical frequency standard
|
|
techniques to physical measurement problems of outstanding fundamental interest. One such mea-
|
|
surement, a HeNe laser version of the Michelson-Morley isotropy of space experiment, has already
|
|
appeared [28]. Other precision experiments underway include: determination of the ground state Lamb-shift using two-photon spectroscopy [9] or construction of a fundamental frequency standard using the same 1S-2S transition [29]; remeasurement of the Rydberg constant using precision atomic beam spectroscopy [30]; precise measurement of metastable and Rydberg energy levels in helium to test the quantum-defect formalism; remeasurement of the relativistic time dilation with vastly higher accuracy; and measurements to set a Hmit on any possible vector anisotropy in the speed of light. These and related stable laser techniques also appear relevant to interferometric gravity wave detectors [31] and some methods of detecting the influence of parity-nonconservation effects [32].
|
|
|
|
References
|
|
[1] J. L. Hall, in Atomic Physics 3, Ed. by S. J. Smith and G.
|
|
K. Walters (Plenum, New York, 1973), p. 615.
|
|
[2] 7 X lO'l S. N. Bagev, L. S. Vasilenko, V. G. Gol'dort, A. K. Dmitriev and A. S. Dychkov, Sov. J. Quantum Electron. 7, 665 (1977).
|
|
[3] S. N. Bagev and V. P. Chebotayev, Appl. Phys. 7, 71 (1975). [4] C. Freed and R. G. O'Donnell, Metrologia 13, 151 (1977). [5] C. J. Borde, M. Ouhayoun, A. vanLerberghe, C. Salamon, S.
|
|
Avrillier, C. D. Cantrell, and J. Borde, in Laser Spectroscopy IV, Ed. by H. Walther and K. W. Rothe (SpringerVerlag, Heidelberg, 1979), p. 142.
|
|
|
|
[6] L. A. Hackel, R. P. Hackel, and S. Ezekiel, Metrologia 13.
|
|
171 (1977). [7] P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder,
|
|
IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
|
|
[8] G. R. Hanes and K. M. Baird, Metrologia 5, 32 (1969). W. G.
|
|
Schwitzer, E. G. Kessler, R. D. Deslattes, H. P. Laver, and J. R. Whetstone, Appl. Opt. 12, 2927 (1973). J. M.
|
|
Chartier, J. Helmcke, and J. A. Wallai-d, IEEE Ti-ans. In-
|
|
strum. Meas. IM-25, 450 (1976).
|
|
[9] See for example A. I. Ferguson, J. E. M. Goldsmith, T. W. Hansch, and E. W. Weber, in Laser Spectroscopy FV, op.
|
|
cit., p. 31.
|
|
[10] R. L. Barger, T. C. English, and J. B. West. Opt. Commun.
|
|
18, 58 (1976).
|
|
|
|
43
|
|
|
|
[11] J. Helmcke, S. A. Lee, and J. L. Hall, Appl. Opt. 21, 1686
|
|
(1982).
|
|
[12] R. W. P. Drever, private communication. [13] R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G.
|
|
M. Ford, and A. J. Munley, in preparation. [14] Y. V. Baklanov, B. Y. Dubetsky, and V. P. Chebotayev,
|
|
Appl. Phys. 9, 171 (1976). [15] S. A. Lee, J. Helmcke, and J. L. Hall, in Laser Spectroscopy
|
|
IV, op. cit, p. 130. [16] J. C. Berquist, S. A. Lee, and J. L. Hall, Phys. Rev. Lett.
|
|
38, 159 (1977). [17] J. L. Hall, C. J. Borde, and K. Uehara, Phys. Rev. Lett. 37,
|
|
1339 (1976).
|
|
[18] J. L. Hall, C. Borde, and C. V. Kunasz, Bull. Am. Phys.
|
|
Soc. 19, 448 (1974). [19] R. L. Barger, Opt. Lett. 6, 145 (1980). [20] D. Halford, H. Hellwig, and D. Glaze, private communication.
|
|
[21] J. L. Hall, Opt. Commun. 18, 62 (1976).
|
|
|
|
[22] T. E. Gough, R. E. Miller, and G. Scoles, Appl. Phys. Lett. 30, 338 (1977).
|
|
[23] G. C. Bjorklund, Opt. Lett. 5, 15 (1979). [24] L. Hollberg, T. Baer, H. Robinson, and J. L. Hall, Appl.
|
|
Phys. Lett. 39, 680 (1981).
|
|
[25] T. W. Hansch and A. Schawlow, Opt. Commun. 13, 68 (1975). [26] J. E. Bjorkholm, R. R. Freeman, and D. B. Pearson, Phys.
|
|
Rev. 23, 491 (1981).
|
|
[27] D. Wineland and H. Dehmelt, Bull. Am. Phys. Soc. 20, 637
|
|
(1975).
|
|
[28] A. Brillet and J. L. Hall. Phys. Rev. Lett. 42, 549 (1979).
|
|
[29] E. V. Baklanov and V. P. Chebotalyev, Opt. Commun. 12,
|
|
312 (1974).
|
|
[30] C. Weiman, private communication; W. L. Lichten, private
|
|
communication. (See also these proceedings.)
|
|
[31] R. W. P. Drever and K. S. Thorne, private communication: P. L. Bender and J. E. Faller, private communication.
|
|
[32] I. B. Khriplovich, JETP Lett. 20 315 (1974).
|
|
|
|
44
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Measurement of Frequency Differences of Up to 170 GHz Between Visible
|
|
Laser Lines Using Metal-lnsulator-Metal Point Contact Diodes*
|
|
|
|
H.-U. Daniel^ M. Steiner^^ and H. Walther^'^^
|
|
Frequency differences of up to 170 GHz between the lines of a cw dye laser and a krypton laser at 568 nm were measured by mixing laser and microwave radiation in a metal-insulator-metal point con-
|
|
tact diode. The beat signals exhibit good signal-to-noise ratio and no frequency "roll-off is observed
|
|
when increasing the laser frequency difference from a few hundred MHz to 170 GHz. It follows that
|
|
the point contact diode could be used at still much higher difference frequencies. Furthermore, these investigations show a diode response which is different at microwave and visible laser frequencies. Video detection experiments performed in the visible show the influence of thermal phenomena in the diode junction having a roll-off frequency of a few megahertz.
|
|
Key words: frequency measurements; heterodyne spectroscopy; metal-insulator-metal diodes.
|
|
|
|
1 . Introduction
|
|
|
|
Metal-insulator-metal point contact diodes (MIM diodes) have already been weW knovi^n for about 15 years as
|
|
effective nonlinear mixers and harmonic generators for
|
|
infrared and microwave radiation [1]. On these grounds
|
|
they have been extensively used for absolute measurements of infrared laser frequencies [2] and for precision infrared heterodyne spectroscopy (see, for example, Ref.
|
|
MIM [3]). HoM^ever, until recently all efforts to use
|
|
diodes in the visible spectrum for these purposes have failed [4], thus causing a rather extensive discussion on the diode action in general. Free electron tunnelling [5], thermally enhanced field emission [6], and photoexcitation of tunnel electrons [7] are but a few of the possible mechanisms proposed.
|
|
|
|
This contribution reports on recent efforts made by the
|
|
|
|
authors [8, 9] to extend the range of application of MIM
|
|
diodes into the visible spectrum. By mixing the radiation
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|
of a cw ring dye laser and a krypton laser at 568 nm with
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|
an appropriate microwave frequency it could be demon-
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|
MIM strated that
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|
diodes are valuable tools for difference
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frequency measurements even in the visible: The
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170 GHz we report is the largest frequency difference
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|
yet measured between two visible laser lines. Further-
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more, our results strongly indicate different mechanisms
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|
to be effective in the microwave and visible frequency
|
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|
ranges. These different mechanisms are found to cause
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serious signal losses when mixing microwaves and visible
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laser radiation and, therefore, make it difficult to use
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microwave harmonics simultaneously generated in the
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diode.
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2. Experimental
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Video detection experiments could be done simply by focusing the multi-mode radiation of an argon ion laser (514.6 nm) onto the point contact diode and measuring
|
|
the laser-induced diode currents at the kilohertz chopping frequencies and/or at the intermode beat frequen-
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*Work supported in part by the Deutsche Forschungsgemeinschaft. tMax-Planck-Institut f. Quantenoptik, D-8046 Garching, Fed. Rep. Germany. ttSektion Physik, Universitat Miinchen, D-8046 Garching, Fed. Rep. Germany.
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cies. Mixing experiments, however, were partly performed with an optically pumped sodium dimer ring laser emitting two or more lines simultaneously and in the single-mode regime [8]. As this set-up showed certain drawbacks, the main part of the mixing experiments was done with the apparatus schematically shown in Fig. 1
|
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OSA
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Figure 1. Block diagram of the experimenial set-up.
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[9]. The dye laser used was an actively stabilized ring
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dye laser (Coherent 699) providing a single-mode output
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mW of up to 200
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at 568 nm (Rhodamine 6G). A single-
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mode krypton ion laser (Spectra Physics 171 with intra-
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cavity etalon) which was locked to a temperature con-
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|
trolled confocal Invar Fabry-Perot cavity, served as a second laser source. Additionally its intensity was stabil-
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ized using an external ADP crystal device. The detuning
|
|
of the dye laser emission relative to the fixed kiypton laser frequency could be monitored by measuring an lo absorption spectrum (see Fig. 1) and comparing it with the iodine line atlas of Gerstenkorn and Luc [10].
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Both laser beams were adjusted for optimal collinear-
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ity, expanded in a telescope and finally focused onto the diode by means of a microscope objective. The diode itself consisted of a 25 ixm thick tungsten wire with an electrolytically etched tip (radius of curvature 50-80 nm)
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in mechanically adjustable contact with a polished cobalt
|
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45
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platelet. This electrode material seemed to offer a some-
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what superior stabihty compared with previously used
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metals.
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Microwave frequencies tunable from 60 to 90 GHz
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|
|
were produced by a wobble generator (Marconi Model
|
|
BWO 6600/1 with a Siemens backward wave oscillator
|
|
6655, peak output power 50 mW) and could be controlled
|
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|
|
by a three-stage frequency locking stabilization scheme
|
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which has been described elsewhere [8]. In the G-band a
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reflex klystron (Varian VRT 2122 A) provided an ap-
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|
mW proximate power of 10
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at 170 ± 1 GHz; however, the
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spectral density was rather low since, owing to a power
|
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supply failure, the line width of the klystron emission
|
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|
was 10 MHz. The microwave frequencies were coupled
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MIM into the
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diode while it stood in a small groove in the
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|
front end of a suitably twisted piece of waveguide. In the
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E-band a small gold reflector at an appropriate distance
|
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|
from the diode and the waveguide helped to form a fa-
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|
vorable cavity-like field distribution.
|
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|
|
Beat signals detected by the MIM diode were amplified (Avantek AMT 2006 M, 0.1-2 GHz, 49.5 dB gain, 4 dB
|
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|
noise figure) and then measured in a microwave spectrum
|
|
|
|
analyzer. Ovdng to mechanical chopping of the laser
|
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|
|
beams the video output of each spectrum analyzer scan
|
|
could be detected by lock-in techniques. When the laser
|
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|
|
difference frequency and a microwave harmonic were
|
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|
|
mixed, a digital signal averager following the lock-in am-
|
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|
|
plifier had to be applied to recover the beat signals from
|
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|
noise.
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|
|
3. Frequency Difference Measurements
|
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|
|
For reasons yet to be explained we always found the
|
|
optimal detection of visible laser light in low ohmic point
|
|
contact diodes. Evidently, this caused signal losses when mixing laser radiation and microwaves because the latter are best detected by highly nonlinear, i.e., high-resis-
|
|
tance, diode junctions. Consequently, mixing experiments always had to begin with the observation of a low
|
|
frequency beat note (about 40 dB above noise) between
|
|
the two laser lines with a low resistance (10-20 O) MIM
|
|
diode. Increasing the diode resistance subsequently led to improved microwave detection and finally to reproducible observation of laser-microwave beat signals. These beats were obtained within a wide range of diode resis-
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|
|
|
tances, but for stability reasons the best results fell into the 30-50 fl range. Furthermore, most effective mixing
|
|
was achieved when the detected dc signals of laser and microwave intensity showed positive polarity.
|
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|
|
Figure 2 shows mixing signals between the two dif-
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|
ferent laser hnes and the 170 GHz klystron emission ob-
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|
tained with a 30 ohm diode. The best signal-to-noise
|
|
ratio observed was 10 dB. We found similar mixing signals at a few hundred MHz as well as in the whole band
|
|
|
|
from 60 to 90 GHz with amplitudes up to 14 dB above
|
|
|
|
noise. This, however, certainly does not indicate a fre- ^
|
|
|
|
quency roll-off, but has to be attributed to the mentioned
|
|
|
|
fact that the klystron emission hne width at 170 GHz
|
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|
|
BWO was nearly a hundred times as broad as the
|
|
|
|
emis-
|
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|
|
sion Hne width.
|
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|
|
All beat signals between laser lines and fundamental microwave frequencies were observed by real-time spectrum analysis and without the need of signal averaging. Averaging was found necessary, however, in the case of mixing the laser light with a second harmonic of a microwave frequency generated simultaneously on the diode. The beat signals achieved between two green Na2 dimer laser lines (frequency difference 122 GHz) and the
|
|
second harmonic of a 61 GHz microwave frequency were
|
|
heavily buried in noise (about -20 dB). This conversion loss of more than 30 dB is considerably higher than the loss usually observed when generating microwave har-
|
|
monics in a MIM diode. As mentioned above it has to be
|
|
ascribed to the low-resistance diode characteristic neces-
|
|
sary for the light mixing experiment. Consequently, the latter still turns out to be a major obstacle in mixing the laser light with microwave harmonics; solving this problem would open an even vdder range of application to
|
|
MIM point contact structures.
|
|
|
|
4. Detection IVIechanisms
|
|
While elastic electron tunnelling has finally been established as the diode mechanism effective in the infrared and millimeter ranges [11], the response of the diode to visible laser hght is still under discussion. Here thermal,
|
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|
n I I I >iM|
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|
—I
|
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|
iM| I
|
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|
|
I
|
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|
11
|
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|
r
|
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|
OdB
|
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|
"ni
|
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|
—1 I
|
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|
1 1 1 III
|
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|
|
-20
|
|
|
|
-AO
|
|
|
|
Figure 2. Beat signal obtained by mixing the light of the dye laser and the krypton laser with a microwave frequency of 170 GHz. a: photograph of the beat signal (central peak between two strong noise bursts) taken from spectrum analyzer (vertical scale 10 dB/div, intermediate frequency 409 MHz, IF bandwidth 1 MHz, scan width 5 MHz/div, scan time 5 msl MHz), b: the same signal after phase-sensitive detection.
|
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|
|
-60 -
|
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|
-J
|
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I
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|
I 1 1 1 III
|
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|
I
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|
0,1MHz
|
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|
I
|
|
1MHz
|
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|
|
10MHz 100MHz
|
|
|
|
FREQUENCY DIFFERENCE
|
|
|
|
1GHz
|
|
|
|
Figure 3. Laser induced diode current increase versus frequeticy of the laser intensity modulation (diode resistance 50 ohm).
|
|
|
|
46
|
|
|
|
photoemissive, and geometrical phenomena are involved, thus leading to rather complex diode behaviour.
|
|
Two especially interesting findings which have been
|
|
discussed in detail elsewhere [8] should still be mentioned here: In video detection experiments there is frequency roll-off observed in the detection characteristic of
|
|
MIM diodes (Fig. 3), and there can be laser driven
|
|
currents of different polarity depending on their modulation frequency [8]. Both indicate that there is a substan-
|
|
tial change in the diode action when going from near dc detection, where most of the investigations were performed (see, for example, Ref. [5]), to true mixing
|
|
conditions.
|
|
The results given in Fig. 3 were obtained by detecting the diode current induced by multimode argon ion laser radiation (514.6 nm) in a 50 ohm junction. Between
|
|
50 kHz and 80 MHz the beam was modulated in an
|
|
acousto-optical device; higher intermediate frequencies were produced by intermode beat signals. While the high frequency roll-off is due to diode mismatch, the low fre-
|
|
quency decrease of 30 dB is caused by the time characteristic of the thermal diode response. The solid line drawn in this frequency range (Fig. 3) displays the theoretical tunnelling current driven by thermal modula-
|
|
tions of a whisker tip with a 1.7 MHz thermal cut-off
|
|
frequency [6, 8]. In addition, noise temperature measurements give tip temperatures between 500 and 1000 K. It is therefore concluded that thermal heating of the junction provides the main contribution to the diode response below 100 MHz. At higher frequency differences it probably assists the field emission of electrons at both sides of the contact [8, 12], thus causing the polarity changes mentioned above. So the main difference between the observed diode response to infrared and microwave frequencies and to visible laser light seems to consist of thermal influences in the latter case.
|
|
5. Summary
|
|
It has been shown that MIM point contact diodes can
|
|
be used as effective nonlinear mixer elements for visible laser light and microwave frequencies. The signal-tonoise ratio can be further improved by using more powerful and frequency stabilized microwave sources and
|
|
|
|
a better mechanical adjustment for the diode. There was no frequency roll-off observed in the mixing experiments; this suggests that for the measurement of larger frequency differences the microwaves can be replaced by infrared or far-infrared laser frequencies, which are known to couple even better to the diode whisker. Such a link between the visible and infrared regions is of considerable importance for metrology. In the visible spectrum the range of frequency differences now obtainable with
|
|
MIM diode mixers is far wider than before, which will
|
|
make it possible to exploit the obvious advantages of frequency measurements as compared to wavelength meas-
|
|
urements. The simphcity of the MIM diode technology
|
|
and already widespread knowledge of it should be of particular advantage compared with, for example, the use of integrated Schottky mixers.
|
|
References
|
|
[1] L. 0. Hocker and A. Javan, Phys. Lett. 26A, 255 (1968). [2] K. M. Evenson, D. A. Jennings, F. R. Petersen, and .J. S.
|
|
Wells, in Laser Spectroscopy III, Ed. by J. Hall and J. L.
|
|
Carlsten (Springer, Berlin, New York, 1977) p. 56.
|
|
[3] J. S. Wells, G. E. Streit, and F. R. Petersen, Opt. Commun.
|
|
19, 248 (1976). [4] D. A. Jennings, F. R. Petersen, and K. M. Evenson, in Laser
|
|
Spectroscopy IV, Ed. by H. Walther and K. W. Rothe
|
|
(Springer, Berlin, 1979) p. 39.
|
|
[5] S. M. Faris, T. K. Gustafson, and J. C. Wiesner, IEEE J.
|
|
(Quantum Electron. QE-9, 737 (1973). [6] A. A. Lucas and P. H. Cutler, Solid State Commun. 13, 361
|
|
(1973).
|
|
[7] G. M. Elchinger, A. Sanchez, C. F. Davis, Jr., and A. Javan, J. Appl. Phys. 47, 591 (1976).
|
|
[8] H.-U. Daniel, M. Steiner, and H. Walther, Appl. Phys. 25, 7
|
|
(1981).
|
|
[9] H.-U. Daniel, M. Steiner, and H. Walther, Appl. Phys. 26,
|
|
19 (1981).
|
|
[10] S. Gerstenkorn and P. Luc, Atlas du spectre d'absorption de la molecule de I'iode, U800-20000 cw"', (Editions du
|
|
CNRS, Paris 1978).
|
|
[11] A. Sanchez, C. F. Davis, Jr., K. C. Liu, and A. Javan, J. Appl. Phys. 49, 5270 (1978).
|
|
[12] M. J. G. Lee, R. Reifenberger, E. S. Robbins, and H. G. Lindenmayr, J. Appl. Phys. 51, 4996 (1980).
|
|
|
|
47
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Precision Frequency Metrology for Lasers in the Visible and Application to Atomic Hydrogen
|
|
B. Burghardt, H. Hoeffgen, G. Meisel, W. Reinert, and B. Vowinkel
|
|
Institut fur Angewandte Physik and Radioastronomisches Institut, Oniversitat Bonn, D-5300 Bonn, F.R.G.
|
|
|
|
A multi-step method is discussed that permits the determination of frequency differences between A lasers in the visible in cases where the beat frequency is too large for direct detection. step width of
|
|
80 GHz is used; the beat signal is picked up with millimeter-wave GaAs photodiodes. The resulting beat signals can be measured without further smoothing using a frequency counter. We report on ex-
|
|
periments with atomic hydrogen, applying the method to measure transition frequencies aiming to determine the Rydberg frequency and the electron/proton mass ratio with increased precision.
|
|
Key words: atomic hydrogen transitions; electron-proton mass ratio; frequency measurement for visible laser radiation; Rydberg frequency.
|
|
|
|
1. Introduction
|
|
Heterodyne techniques have been proven to be extremely powerful in all fields of frequency metrology. For optical laser frequencies this principle is applied by superimposing the parallel beams of the lasers so that the beat frequency can be detected via a photodiode. The result is the difference betw^een the frequencies of the two lasers. This method is widely used to determine the spacings, e.g., between hyperfine components and other
|
|
details in optical spectra [1]. An upper limit for the size
|
|
of the measurable spacings is set by the reaction speed of the diode. Commercial fast photodiodes have cut-off fre-
|
|
quencies ranging from 5 to about 10 GHz with a fast fall-
|
|
off if they are used at higher frequencies.
|
|
An alternative task is to determine the absolute fre-
|
|
quency of laser radiation. The laser can be one that has been tuned to some atomic or molecular transition of interest or it may be a new reference laser with a stable but not yet accurately known frequency. There are three ways to determine the frequency of such a laser: First, the laser can be compared with the frequency of one or several other lasers through a frequency chain that
|
|
MIM reaches into the visible [2]. Nonlinear crystals and
|
|
diodes can be used for this purpose though the method is difficult to apply routinely since it requires that phase matching conditions for laser radiation over a very wide range be met. The nonlinear efficiencies of crystals that meet such conditions are small, so that in many cases the
|
|
signals may be too small. Even if this method can be ap-
|
|
plied to selected cases only, its great value lies in the fact that it can be used to establish one or several reference laser frequencies in the visible with high accuracy.
|
|
The second method is to compare the wavelength of the laser v\dth unknown frequency vdth that of a laser of known frequency [3]. The main problems arise from the fact that in an interferometric wavelength comparison geometric properties of the two laser fields such as their parallelism and wavefront shape influence the result systematically. Some progress has been achieved in this field by carefully controlling the laser beam parameters
|
|
[4].
|
|
|
|
2. Optical Laser Frequency Measurement
|
|
|
|
A third method by which to determine the absolute fre-
|
|
quency of visible laser radiation is discussed in this paper. It makes use of a reference laser with well-known frequency and a beat frequency determination. Thus it avoids the dangers of interferometric methods and gains from the fact that beat frequencies are not shifted if the two superimposed beams are out of parallelism. The obvious principle of the method is to determine the frequency difference between the reference laser and the laser whose frequency is to be determined. The difference is added to or subtracted from the reference frequency for the final result. It is the scope of this paper to
|
|
discuss how this method can be applied in practice.
|
|
|
|
Clearly, the reference frequency should be close to the
|
|
|
|
unknown frequency so that the beat frequency is low and
|
|
|
|
thus easily measurable. The octave of visible light, how-
|
|
|
|
ever, spans about 375 THz. If a set of, e.g., 10 reference
|
|
|
|
lasers with almost equally spaced frequencies is estab-
|
|
|
|
lished vdthin this band, the difference vdth respect to an
|
|
|
|
arbitrarily chosen unknown frequency can be as large as
|
|
|
|
20 THz approximately. At present the only well-known
|
|
|
|
reference lasers are stabilized to iodine transitions at 633
|
|
|
|
nm (HeNe, [5]) and 514 nm (Ar, [6]). There are no photo-
|
|
|
|
diodes that are fast enough to follow a 10 THz beat oscil-
|
|
|
|
A lation.
|
|
|
|
solution to the problem of measuring such a
|
|
|
|
high difference frequency is to cut it into many smaller
|
|
|
|
differences that can be measured separately. This is
|
|
|
|
achieved by using two cw dye lasers as interpolating os-
|
|
|
|
cillators. The principle is schematically presented in Fig.
|
|
|
|
1: Laser 1 has the unknown (or only approximately
|
|
|
|
knovra) frequency Vj. . Dye laser 2 is tuned to a frequency V2 so that (v2 - Vj:) is measurable. Dye laser 3 in turn is
|
|
tuned to V4, etc., until Vref is reached. The sum of all par-
|
|
|
|
tial differences is the final large difference.
|
|
|
|
It is clear that the practical application of this scheme
|
|
|
|
requires that the step width be as high as possible in
|
|
|
|
order to avoid excessively large step numbers and cumu-
|
|
|
|
We lative errors.
|
|
|
|
found a step width of 80 GHz (approxi-
|
|
|
|
mately 1 A at 6OOOA) a reasonable compromise between
|
|
|
|
A costs and efficiency of the method [7].
|
|
|
|
special GaAs
|
|
|
|
49
|
|
|
|
Figure 1. Schematic diagram to illustrate the procedure using two interpolating oscillators (lasers 2 and 3) to close the gap between laser 1 of unknow7i frequency ( vj and a reference
|
|
laser ( Vy^f).
|
|
|
|
Figure 3. Schematic diagram of the E-band heat frequency
|
|
detector,
|
|
|
|
2 \im
|
|
|
|
Figure 2. Cross section of the GaAs Schottky photodiode used to detect beat signals of 80 GHz and over.
|
|
|
|
Schottky diode was used to pick up the beat oscillation
|
|
|
|
[8]. The active area of the diode has been enlarged to in-
|
|
|
|
crease the beat signal. The resulting signal/background
|
|
|
|
mW level was high, namely 40 db for two 2
|
|
|
|
laser beams.
|
|
|
|
Figure 2 is a cutaway view of a single diode. Several
|
|
|
|
thousand are manufactured on a diode chip which is
|
|
|
|
mounted inside an E-band wave guide light detector
|
|
|
|
mW (Fig. 3). The diodes were used up to a 70
|
|
|
|
cw light
|
|
|
|
level focused to a spot size of 10 ixm vdthout damage to
|
|
|
|
the diode.
|
|
|
|
3. Application to Hydrogen Transitions
|
|
|
|
An experiment is being prepared to measure the fre-
|
|
quency of the hydrogen H„ transition and of other transi-
|
|
|
|
tions in this way. For He, the HeNe reference laser will be used, which requires about 210 steps of 80 GHz each. The expected uncertainty is 0. 1 to 1 kHz per step resulting in an overall error of 20 to 200 kHz for the total difference with respect to the HeNe laser. The other
|
|
main contribution to the error arises from the uncertainty to which laser 1 (which in this case is identical to
|
|
laser 3) can be tuned to the center of the 30 MHz wide H„ A transition. conservative estimate of this uncertainty is
|
|
1% of the line width or 300 kHz [9]; with careful control
|
|
of the atomic lineshape and the laser light distribution the uncertainty might be as low as 10"^ of the linewidth or 30 kHz. Altogether it is planned to determine the He
|
|
frequency to within 50 to 500 kHz or with a relative uncertainty of 10^ to 10^^°. The result will be an improved
|
|
value of the Rydberg frequency, R^c with an accuracy
|
|
approaching the 10" level.
|
|
The experiment is performed with the "free" atoms of an atomic beam in order to reduce any perturbations to the lowest possible level. The Hght interaction region is designed to avoid Doppler effects, making use of two spatially separated light fields from two exactly counterrunning laser beams [10]. This method ensures that the
|
|
resulting Lamb dip cannot be shifted by non-perfect alignment of the atomic beam with respect to the laser.
|
|
Other atomic hydrogen transitions that are within the
|
|
range of available cw lasers are, e.g.. Ha (4860 A) and H^
|
|
(4341 A). Since the 4p and 5p states involved have considerably longer natural lifetimes than the 3p state associated with the Ha transition, the accuracy might even be higher. If one accurately measured hydrogen frequency is divided by another, the Rydberg frequency as a leading factor is eliminated, which allows interesting tests for the remaining calculated factors [11].
|
|
In another experiment we are trying to observe the
|
|
two-photon transition from 2s to 7s, 8s or 9s of hydrogen which requires readily available laser radiation between 750 and 800 nm. Besides an absolute frequency determination, the experiment aims to measure the isotope shift in order to improve the accuracy of the proton/electron mass ratio.
|
|
|
|
50
|
|
|
|
References
|
|
[1] G. Nowicki, H. Bekk, S. Goring, A. Hauser, H. Rebel, and
|
|
G. Schatz, Phys. Rev. C 18, 2369 (1978).
|
|
[2] K. M. Baird, K. M. Evenson, G. R. Hanes, D. A. Jennings, and F. R. Petersen, Opt. Lett. 4, 263 (1979).
|
|
[3] H. P. Layer, R. D. Deslattes, and W. G. Schweitzer, Jr.,
|
|
Appl. Opt. 15, 734 (1976). [4] J. P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A.
|
|
Szoke, F. Zernike, P. H. Lee, and A. Javan, Appl. Opt. 20, 736 (1981), and references therein. [5] F. Bayer-Helms, Ed., PTB-Bericht ME-17 (Physikalisch-
|
|
|
|
Technische Bundesanstalt, 1977).
|
|
[6] F. Spieweck, IEEE Trans. Instrum. Meas. IM-29, 361
|
|
(1980).
|
|
[7] B. Burghardt, H. Hoeffgen, G. Meisel, W. Reinert, and B. Vowinkel, to be published
|
|
[8] B. Burghardt, H. Hoeffgen, G. Meisel, W. Reinert, and B. Vowinkel, Appl. Phys. Lett. 35, 498 (1979).
|
|
[9] B. Burghardt, M. Dubke, W. Jitschin, and G. Meisel, Phys.
|
|
Lett. 69A, 93 (1978).
|
|
[10] B. Burghardt, H. Hoeffgen, H. Kritz, and G. Meisel, PTBBericht E-18 (Physikalisch-Technische Bundesanstalt,
|
|
1981).
|
|
[11] G. W. Erickson, J. Phys. Chem. Ref. Data 6, 831 (1977).
|
|
|
|
51
|
|
|
|
1
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
System for Light Velocity IVIeasurement at NRLIVI
|
|
K. Tanaka, T. Sakurai, N. Ito, T. Kurosawa, A. Morinaga, and S. iwasaki
|
|
National Research Laboratory of Metrology 1-4, 1-chome, Umezono, Sakura-Mura, Niihari-Gun, IbarakI 305, Japan
|
|
A system for making an absolute measurement of the wavelength and frequency of a stabilized
|
|
carbon-dioxide laser is under construction. The wavelength has been measured by an up-conversion technique using Proustite vwth reference to an iodine stabilized laser. The determined value is 9.31724631 (im with a standard error of the mean of 1.4 x 10^* of the wavelength and the systematic uncertainty is roughly estimated to be 3 x 10"^ of the wavelength. For the frequency measurement, a water vapor laser and an optically pumped alcohol laser have been constructed. Tungsten-nickel and tungsten-cobalt point contact diodes with precision mounts as harmonic generators and mixers have been developed and used for evaluating the stability of the carbon-dioxide laser by beat frequency counting.
|
|
Key words: CO2 laser; light velocity; optical frequency difference; wavelength.
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|
1 . Introduction
|
|
Since a precision value of the velocity of light was reported by Evenson et al. [1] at the fifth meeting of the
|
|
CCDM in 1973, the value was confirmed by Blaney et al.
|
|
[2] and Baird et al. [3]. The present authors, considering the likelihood that a definition of the meter based on the velocity of light will be adopted in the very near future, have been developing a system, which is shown in Fig. 1, for measuring the absolute wavelength and frequency of a carbon-dioxide laser to reconfirm the light velocity and to provide for the establishment of a future wavelength and optical frequency standard.
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X-BAND KLYSTRON (lOGHz)
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E-BAND KLYSTRON tSSGHz)
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BEAT
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(O.93GH2)
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' ^
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BEAT (-0.05 GHz)
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H — ICH3OH LASER
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^
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|
(ll94GKzl|
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K - BAND KLYSTRON 1 25 GHz)
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J
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|H;0 LASER
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'
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BEAT
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>
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®
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V (~ 0.05 GHz)
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1
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y
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(10718 GHz)
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I
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K-BAND KLYSTRON 122 GHz)
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|C02 LASER (32176 GHz
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I
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9.3
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HIGH POWER He-Ne LASER LOCKED TO I2 STABILIZED LASER (633 nm)
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WAVELENGTH )>
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FABRY -PEROT INTERFEROMETER
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2. Wavelength Measurement
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In order to measure the absolute wavelength of a 9.3 |jim stabilized CO2 laser, 9.3 |xm radiation is upconverted to deep red 0.679 p.m radiation generated by difference frequency mixing vdth the radiation from a 0.633 |xm stabilized He-Ne laser in a nonlinear crystal,
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Proustite (AgsAsSs) [4, 5].
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As the speed of light is independent of wavelength in vacuum, the relation I/X9.3 = l/Xo.ess ~ 1/^.679 holds. The wavelength of 9.3 ixm can be calculated from the two visible wavelengths, if they are knowni. The wavelength of 0.679 |xm is measured with a pressure scanned Fabry-
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Perot interferometer vdth reference to a 0.633 ixm offset
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lock He-Ne laser whose wavelength is determined from the ^^l2 stabilized He-Ne laser.
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The experimental system is schematically shovra in
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|
m Fig. 2. The 1.6 long CO2 laser having an intracavity
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R CO2 cell is stabilized to the
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(12) line of the 9.4 |xm
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band by the Javan-Freed method, locking to the zero
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crossing point of the first derivative signal of 4.3 ixm sa-
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|
turated fluoresence. TEMoo output power of this laser is
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W typically 0.3 (after a chopper), and its frequency sta-
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bility is 3 X 10-1^.
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stab. C02 loser
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^ 66^^
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(606nm)
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^
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Figure 1. System for light velocity measurement.
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Figure 2. Experimental system for tvavelength measurement of
|
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carbon-dioxide laser.
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53
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.
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m The 2 long 0.633 |xm He-Ne laser having a Fox-
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Smith type mode selector is operated at a single fre-
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|
quency [6]. Its frequency is + 4.8 MHz offset locked,
|
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with a relative stability of 1 x 10"^\ to the i-component
|
|
of the R(127) line of a ^^'^h stabilized He-Ne laser, which has a reproducibility of 6 x 10"^^ [7]. The absolute
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|
|
wavelength of this laser locked to the i-component of ^^^la
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has been evaluated to be 0.632 991 400 0 jjim with a standard error of the mean of 3 x 10"^ of the wavelength
|
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|
[8]. As we have confirmed that the measured value
|
|
agrees with the recommended value of the CCDM in 1973
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|
|
within the uncertainty of the measurement, the absolute
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vacuum wavelength of the offset locked laser is deter-
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|
mined as 0.632 991 392 6 jxm based on the recommended
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value of the iodine stabilized laser. The usual output
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mW power of the TEMqo mode of this laser is 5
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|
whereas
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that of the iodine stabilized laser is 30 |jlW.
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The beams of both the CO2 laser and the He-Ne laser
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mm are weakly focused into the center of a 6
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|
|
long Prous-
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|
m tite crystal so that the same confocal parameter of 0.2
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can be obtained. The Proustite is cut and polished so
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|
that Type II phase matching is realized by angle tuning,
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and it is positioned in a liquid nitrogen cryostat cooled to
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77 K.
|
|
W The 0.679 ixm radiation of about 10"^ is introduced to
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|
the Fabry-Perot interferometer along with that from the
|
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offset locked He-Ne laser. A Glan-Thompson prism and a
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grating monochrometer are used for suppressing the in-
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A tensity of background 0.633 |xm radiation.
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plastic
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|
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diffuser and a set of lenses are also used for achieving uni-
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|
form illumination onto the Fabry-Perot interferometer.
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|
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Scanning of the optical path length of the interferome-
|
|
ter is made in a nearly linear fashion by introducing dry
|
|
nitrogen gas as a supersonic flow into the Fabry-Perot chamber through a needle valve. Simultaneous scanning for both radiations of 0.679 |xm and 0.633 jxm eliminates the systematic error caused by thermal drift and misalignment of the interferometer, or by the difficulty
|
|
in reaUzing the same reference pressure, 4 Pa, when the scanning is started. The combined light of the two lasers is detected by a photomultiplier, and its output signal is suppUed to two lock-in amplifiers, which are synchronized with two light choppers at two different chopping frequencies of 400 Hz and 1 kHz, respectively. The outputs from the two lock-in amplifiers are fed into a 2-pen
|
|
recorder, and a pair of interferograms are obtained on the same chart.
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|
Dispersion of phase change on reflection is eliminated
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|
by using a pair of data of fractional orders which are ob-
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|
tained by using two spacers of the Fabry-Perot inter-
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|
mm ferometers with the lengths of 50
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and 170 mm,
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|
respectively.
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|
Figure 3 shows typical data of Fabry-Perot fringes of 0.679 (xm and 0.633 \xm. The centers of the interference fringes are determined from abscissa readings on both sides of each peak at six intensity levels between 30 and 80% of the peak height. Fractional order number is determined with a standard deviation of 0.001 fringe by extrapolating from four or five peaks by means of a leastsquares method.
|
|
Thirty-three independent measurements were made for
|
|
each of the short and long interferometers respectively. The absolute wavelength of the 0.679 ixm difference frequency radiation was calculated using the method of exact fractions with respect to the "virtual spacer," whose length is the difference between the lengths of the long and short
|
|
interferometers. On the basis of the wavelength of the 0.633 |jLm offset locked laser, the vacuum wavelength of
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|
|
Spacer Length 50nnm
|
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|
|
—- pressure increase
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|
|
Figure 3. Interferograms of 0.679 \im up-converted light and 0.633 |xTO helium-neon laser offset-locked to iodine stabilized
|
|
laser.
|
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|
|
the 0.679 jxm radiation was determined to be 0.679 129 847 4 li-rn with a standard error of the mean of 1 x 10"^ of the wavelength. Thus, the infrared wavelength is calculated to be
|
|
X9,3 = 9.317 246 31 (jLm
|
|
It should be noted that the uncertainty in X.93 is increased by a factor of 14. Therefore, the statistical uncertainty is estimated to be 1.4 x 10"^ of the wavelength as a standard error of the mean. Although the systematic uncertainties are not fully investigated, the uncertainty due to interferometric measurement is roughly estimated to be 3 X 10"^ of the wavelength.
|
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|
|
3. Optically Pumped FIR Laser
|
|
|
|
An optically pumped far-infrared laser shown in Fig. 4
|
|
m has been studied. The 2 long carbon-dioxide laser for
|
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|
|
the pumping is stabilized by an opto-acoustic method.
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|
|
m mm The laser has a 1.5 long, 8
|
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|
|
bore discharge tube. A
|
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|
|
25% CO2, 20% N2 and 55% He gas mixture flows at a
|
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|
|
pressure of 2.0 kPa at the entrance port. A maximum
|
|
W output power of 31 has been obtained under fundamen-
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|
|
m tal mode operation. The FIR laser has a 2.1 long,
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|
|
mm 38.5
|
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|
|
bore Pyrex waveguide. The resonator consists
|
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|
|
mm of a gold coated flat mirror of fused silica with a 2
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|
|
mm entrance hole, and a flat aluminium mirror with a 5
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|
|
CH3OH
|
|
|
|
FIR LASER —2100mm
|
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|
|
M2
|
|
M)
|
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|
|
POWER METER
|
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|
|
PYREX GLASS TUBE
|
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OUT
|
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I
|
|
XQ PYRO- DET.
|
|
•o
|
|
PARAL. SPR.
|
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|
|
CO2 SPE.ANA.
|
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|
|
i WATER
|
|
I
|
|
2000mm
|
|
CO2 LASER
|
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|
|
VjW.OUT
|
|
|
|
- GRATING ,|oo L/mm)
|
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|
|
|
with 3 micro-m.
|
|
\
|
|
|
|
Figure 4. Schematic diagram of optically pumped FIR laser.
|
|
|
|
54
|
|
|
|
FIR coupling hole. Frequency tuning of the resonator is made by a parallel spring mechanism and a micrometer
|
|
driven by a small motor. We have made studies
|
|
concerned with increasing its output power and also sur-
|
|
veyed the most suitable oscillation line for frequency synthesis vdth a water vapor laser and an E-band klystron.
|
|
|
|
4. Water Vapor Laser
|
|
|
|
Two internal-mirror-type water vapor lasers have been
|
|
|
|
constructed to examine the optimum discharge condi-
|
|
|
|
tions, the characteristics of the output beam and the sta-
|
|
|
|
m bilities of output power and frequency. One has a 2.4
|
|
|
|
mm long resonator and a 25
|
|
|
|
bore discharge tube, and the
|
|
|
|
m mm other has a 5.4 long resonator and a 40
|
|
|
|
bore
|
|
|
|
discharge tube. Both lasers have similar designs. The
|
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|
|
laser tube has a water cooling jacket, a copper anode and
|
|
|
|
a water cooled copper hollow cathode in the side arms.
|
|
|
|
The laser resonator is composed of two gold coated Pyrex
|
|
|
|
mirrors which are connected rigidly by four invar rods.
|
|
|
|
Frequency tuning of the resonator can be done by the
|
|
|
|
same mechanism as that of the FIR laser.
|
|
|
|
The water vapor is generated from distilled water in a reservoir and gas additives are supplied to the laser tube from the anode side; they are pumped out from the cathode side by using a continuous gas flow system. The mass flow rate of each gas is regulated by stainless steel needle valves and the gas pressure in the laser tube is adjusted by an exhaust valve.
|
|
|
|
The short resonator laser was used to study the
|
|
|
|
operating characteristics and discharge conditions of the
|
|
|
|
28 |jLm output. It was found that the peak output power
|
|
|
|
was obtained at a discharge current which dissociated
|
|
|
|
mW the H2O rapidly [9]. An output power of about 30
|
|
|
|
is
|
|
|
|
obtained under conditions of a H2O pressure of 80 Pa and
|
|
|
|
a H2 pressure of 120 Pa. The long resonator laser oscil-
|
|
|
|
lated nearly at the condition which was estimated using a
|
|
|
|
scaling law and the lasing condition in the short resona-
|
|
|
|
mW tor laser. The output power was more than 150
|
|
|
|
mul-
|
|
|
|
timode, but it was found that the optimum output power
|
|
|
|
was obtained at a different condition due to different sys-
|
|
|
|
tems of gas flow in the two lasers.
|
|
|
|
For extracting the 28 \xm output from the laser resonator, there are three methods where a coupling hole, an intracavity beam divider and a Michelson-type coupler
|
|
|
|
are used. In the coupling hole method, higher order transverse modes oscillated easily and the polarization
|
|
azimuth of the output beam varied with cavity-scanning [10]. On the other hand, the alignment of the Michelsontype coupler was not easy. Therefore, the output beam was coupled out using a 45° polyethylene intracavity beam divider. The output beam was linearly polarized. The TEMoo mode was obtained easily by inserting an
|
|
|
|
aperture in the cavity.
|
|
|
|
At present, we are aiming to stabilize the frequency of
|
|
|
|
FWHM the laser to the Lamb dip with an
|
|
|
|
of about
|
|
|
|
5 MHz. The frequency of the laser is stabilized by using a
|
|
|
|
piezoelectric translator. To obtain a good reproducibility,
|
|
|
|
the shape of the Lamb dip is being investigated. By
|
|
|
|
analyzing the beat frequency between two water vapor
|
|
|
|
lasers, origins of frequency fluctuations will be clarified.
|
|
|
|
5. M-l-M Point Contact Diode
|
|
|
|
For making precise frequency measurements, we have
|
|
|
|
made tungsten-nickel and tungsten-cobalt point contact
|
|
|
|
A diodes [12, 13] of the metal-insulator-metal type [11].
|
|
|
|
short tungsten wire 25 |xm in diameter was spot welded
|
|
|
|
mm mm to the top of a 2
|
|
|
|
thick and 15
|
|
|
|
long brass rod. The
|
|
|
|
wire was bent and the top of the bent wire was etched by
|
|
|
|
conventional electrolytic polishing techniques. The flat,
|
|
|
|
mm top surfaces of nickel or cobalt posts 30
|
|
|
|
in length and
|
|
|
|
mm 3
|
|
|
|
in diameter were polished so that they had a flat-
|
|
|
|
ness of better than one interference fringe with the
|
|
|
|
589 nm line of a sodium lamp. To obtain resettability and
|
|
|
|
stability of the point contact diode, a precise diode mount
|
|
|
|
which has fine mechanical adjustability and stability of
|
|
|
|
contact pressure, was made. The tungsten-cobalt point
|
|
|
|
contact diode had a S/N ratio 5-10 dB better than that
|
|
|
|
of the tungsten-nickel diode for detecting the rf beat note
|
|
|
|
between harmonics of an X-band klystron and two CO2
|
|
|
|
lasers locked to 9R(24) and 9R(26) lines, respectively, as
|
|
|
|
shown in Fig. 5. This diode was used for measuring the
|
|
|
|
stability of our CO2 laser, which was 3 x 10"^*^.
|
|
|
|
OdBm
|
|
lOd
|
|
|
|
70 MHz
|
|
|
|
0.5 MHz
|
|
|
|
Figure 5. Specty^um of heat signal detected using W-Co point contact diode. Beat is obtained by mixing outputs of X-band klystron and two CO2 lasers locked to 9R(24) and 9R(26) lines.
|
|
|
|
6. Conclusion
|
|
|
|
The absolute wavelength of a frequency stabilized
|
|
|
|
carbon-dioxide laser has been evaluated to be
|
|
|
|
9.31724631 ixm vdth a statistical uncertainty of 1.4 x
|
|
|
|
A 10"^.
|
|
|
|
water vapor laser with a 28 fxm output of
|
|
|
|
mW 150
|
|
|
|
and a tungsten-cobalt point contact diode with a
|
|
|
|
S/N ratio improved by 5-10 dB have been developed.
|
|
We have been studying ways to increase the output of
|
|
|
|
the FIR laser for Hnking the CO2 laser to the cesium fre-
|
|
|
|
quency standard.
|
|
|
|
References
|
|
|
|
[1] K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Daniel-
|
|
son, G. W. Day, R. L. Barger, and J. L. Hall, Phvs. Rev.
|
|
Lett. 29, 1346 (1972).
|
|
[2] T. G. Blaney, C. C. Bradley, G. J. Edwards, B. W. Jolliffe. D. J. E. Knight, W. R. C. Rowley, K. C. Shotton, and P.
|
|
T. Woods, Nature 2.51, 46 (1974); Proc. Soc. London Ser. A
|
|
355, 89 (1977).
|
|
[3] K. M. Baird, D. S. Smith, and B. G. Whitford, Opt. Commun.
|
|
31, 367 (1979).
|
|
[4] K. M. Baird, H. D. Riccius, and K. J. Siemsen, Opt. Commun. 6, 91 (1972).
|
|
[5] B. W. Jolliffe, W. R. C. Rowley, K. C. Shotton, A. J. Wallard, and P. T. Woods, Nature 251, 46 (1974).
|
|
[61 A. Morinaga and K. Tanaka, Jpn. J. Appl. Phys. 17, 881 (1978).
|
|
[7] K. Tanaka, T. Sakurai, and T. Kurosawa, Jpn. J. Appl. Phys. 16, 2071 (1977).
|
|
|
|
55
|
|
|
|
[8] N. Ito and K. Tanaka, Metrologia 14, 47 (1978).
|
|
[9] A. Morinaga and K. Tanaka, IEEE J. Quantum Electron.
|
|
QE-16, 406 (1980).
|
|
[10] A. Morinaga, Appl. Opt. 20, 2395 (1981). [11] L. D. Hocker, D. R. Sokoloff, V. Daneu, A. Szoke, and A.
|
|
|
|
[12] [13]
|
|
|
|
Javan, Appl. Phys. Lett. 12, 401 (1968). T. Kurosawa, T. Sakurai, and K. Tanaka, Appl. Phys.
|
|
36, 751 (1980). T. Kurosawa, A. Kuriyagawa, and K. Tanaka, Bull.
|
|
Res. Lab. Metrology (Japan) 30, 8 (1981).
|
|
|
|
Lett. Natl.
|
|
|
|
56
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Laser Wavelength Measurements and Standards for the Determination of Length
|
|
W. R. C. Rowley
|
|
Division of IVIechanical and Optical Metroloqy
|
|
National Physical Laboratory, Teddington, Middlesex TW11 OLW, U.K.
|
|
|
|
The light emitted by portable stabilized lasers used as wavelength standards for length and spec-
|
|
|
|
troscopic measurements is reproducible to at least three parts in 10
|
|
|
|
and different wavelengths can be
|
|
,
|
|
|
|
intercompared to this level of uncertainty by interferometry. Their absolute wavelength accuracy, lim-
|
|
|
|
ited at present to four parts in 10^ by the ^°Kr standard of the meter, wall be improved at least tenfold
|
|
|
|
by a redefinition of the meter, based on the fixed value 299 792 458 m/s for the speed of light. Length
|
|
|
|
measurements, however, are seldom more accurate than one part in 10^, except in lunar and interplane-
|
|
|
|
tary ranging; although changes in length can be measured to better than one part in 10^'*.
|
|
|
|
Key words: meter definition; precision length measurement; stabilized lasers.
|
|
|
|
1. Introduction
|
|
Developments in precision length and wavelength measurement over the last decade have been dominated to a large extent by laser techniques. For example, the primary unit of length, the meter, was defined in 1960 by
|
|
the wavelength of a krypton-86 transition. By the mid-
|
|
1960' s, stabilized visible helium-neon lasers were becoming widely used for the practical measurement of length by interferometry. The lasers available at that time were
|
|
stabilized to the Lamp dip in the center of the power tun-
|
|
ing curve. The stability and reproducibility, at a few parts in 10^, was significantly worse than that afforded by the ^^Kr lamp. This accuracy was, and to a large extent still is, adequate for the majority of length measurement tasks involving material objects, such as length bars and standard gauges. Gradually laser measurement systems have become so widespread that, for example, the majority of precision length measurement tasks at the National Physical Laboratory are now carried out
|
|
vdth laser interferometer systems.
|
|
Lasers for interferometric measurement are important because of three main characteristics:
|
|
— (a) Temporal coherence Their narrow monochromatic
|
|
bandwidth removes the former path-length restriction of less than 1 m.
|
|
— (b) Spatial coherence The laser emits in a narrow
|
|
beam of almost plane wavefront, so that the light can
|
|
be easily and efficiently used in optical systems.
|
|
— (c) Intensity The amount of light and its efficiency of
|
|
use makes photoelectric detection easy, leading to the application of electronic methods and automated meas-
|
|
urements.
|
|
The length measurement technique that is normally used with lasers is fringe-counting interferometry. Commercial systems are available for general measurements of modest accuracy up to lengths of a few tens of meters. For the highest accuracy, however, purpose-built mechanical systems are mandatory, with particular care
|
|
|
|
taken to avoid alignment, temperature, and refractive in-
|
|
dex errors. The accuracy then attainable when using a
|
|
well calibrated laser standard is as good as can be achieved by using the ^^Kr standard lamp directly. For a 1-m length bar this accuracy is about ±1 x 10"^, or up to
|
|
a factor of two better, at the 99% confidence level [1].
|
|
2. Saturated Absorption Stabilization
|
|
A great advance in the performance of lasers as refer-
|
|
ence standards for length measurement was the introduc-
|
|
tion of the saturated absorption technique of stabilization [2, 3]. It improved the reproducibility of laser standards from being a factor of 10 worse than the '^^Kr lamp to a
|
|
factor of 100 or more better than *^Kr. For several years, two such stabilized laser systems were widely studied and developed. One of them, the 633-nm visible heliumneon laser, stabilized with iodine, is of particular importance because of its direct application to length measurement and its use as a standard for the calibration of other lasers by beat frequency or interferometric wavelength comparison. The other laser system is the methane-stabilized He-Ne laser at 3.39 ixm. Although not so suitable for length measurement, this laser afforded the promise of better stability and reproducibility. It has proved to be a particularly important link in the chain of frequency measurements from the cesium frequency standard towards visible frequencies. The 3.39 p-m wavelength is also close enough to the visible for infrared /visible wavelength measurements to be made. This has enabled the ^^Kr and ^^^Cs standards of length and time to be interrelated, giving a value of the speed of light to the accuracy limitation imposed by the *"Kr standard [4].
|
|
It is usual and convenient for these stabilized lasers to have the saturable absorber within the laser cavity itself. This gives a neat and portable laser system. It is, however, not ideal. The interaction region is too small in diameter so that thermal movement takes the absorbing molecules out of the beam, shortening the effective lifetime; the length of the cell is restricted, so that the pressure of molecules must be raised to give sufficient signal;
|
|
|
|
57
|
|
|
|
and the high beam power density oversaturates the transitions, accentuating any asymmetry. Nevertheless, the performance of these lasers is impressive enough. The stability of a typical internal-cell 633-nm iodine-stabilized He-Ne laser is 3 x 10"^^ for an averaging time of 10 s,
|
|
and the corresponding figure is 1 x 10"^^ for the 3.39 |xm methane-stabilized laser [5].
|
|
A more important measure of performance, however, is
|
|
the reproducibility of the stabilized frequency (or
|
|
wavelength). As a result of many comparisons between
|
|
lasers of different origin, at various times and in various laboratories, it seems that a reproducibility of ±2 x 10"^^ can normally be obtained with internal-cell 633-nm He-
|
|
Ne lasers, provided that the operating conditions are the
|
|
same. The stabilized frequency is affected, for example, by alignment errors, the iodine pressure, the amplitude of frequency modulation, the iodine cell wall temperature, the internal power, etc. The iodine cell must also be free from impurities, such as may result from outgassing during or after sealing-off. From a joint study made re-
|
|
cently between NPL and BIPM, it is clear that such con-
|
|
tamination is not rare, and accounts for at least some of
|
|
the discrepancies of inter-laboratory reproducibility that are occasionally observed. It is clear that the quality of iodine cells needs strict monitoring [6, 7].
|
|
With internal-cell 3.39 iJim methane-stabilized lasers, the methane hyperfine structure is not resolved, and an inter-laboratory reproducibility of only ±3 x 10"'^ has been reported in one study, although the reproducibility figure of ±5 x 10"^^ has been obtained for lasers constructed and compared within one laboratory [5]. By putting the saturable absorber outside the laser cavity, however, the conditions may be optimized, and much better reproducibility achieved. The penalty is a nonportable system. Thus although a reproducibility of 1 x 10"^^ has been reported [5], it has not been possible to confirm, by direct beat-frequency comparison, that this can be achieved internationally with independently con-
|
|
structed laser systems.
|
|
External-cell systems are also advantageous for iodine-stabilized lasers in the visible, and are probably 10
|
|
A or 100 times better than the internal-cell systems.
|
|
number of radiations of the ionized argon and krypton lasers have been thus stabilized for use as wavelength standards, particularly the argon 514-nm line [8]. The orange 612-nm radiation and other transitions of the helium-neon system also show great promise for excellent stability and reproducibility [9]. Indeed, the number of laser wavelength standards that could be realized, particularly by using dye lasers, is almost unlimited. The limit will be set in practice by requirements and resources.
|
|
3. The Role of Wavelength Measurements and Standards
|
|
Wavelength standards are the basis for interferometric length measurement, but they serve a wider purpose. They are, for example, used in spectroscopy, where it is customary to specify absorption and emission lines by their wavelength or wavenumber. The reason for this is historical and a matter of experimental convenience, as spectrographs allow such measurements to be made by interpolation from a reference set of wavelength standards. It would be more fundamental, however, to specify such radiations by the energy difference between the two states involved in the transition. Alternatively, and more conveniently, the frequency of the radiation, which is directly related to energy by the well known relation
|
|
|
|
E = /iv, is more fundamental than wavelength. I hope
|
|
and expect that there will be a gradual changeover from the specification of wavelength or wavenumber to the identification of spectral transitions by their frequency. Thus one should perhaps talk about laser frequency standards rather than laser wavelength standards.
|
|
In comparing similar stabilized lasers to measure their reproducibility, beat frequency techniques are used. These are rapi'd, convenient and precise. Unfortunately it is not yet possible to use beat frequencies in the general case to compare two lasers operating on completely different spectral transitions. The frequency differences are too great to be detected so easily. It is possible to work out schemes to overcome this problem using non-linear crystals as mixers and harmonic generators, synthesizing the difference frequency approximately from infrared and microwave oscillators. The final mixer/detector need then only generate a low-frequency beat. At present, however, it is not clear whether such schemes will be viable for more than a few visible radiations of special interest. The alternative well-established technique is interferometric wavelength comparison. Although widely applicable, it is unfortunately subject to a number of practical limitations that introduce errors and thus limit the accuracy. Nevertheless, accuracies of a few parts in 10^^ have been achieved [10]. Wavelength comparison is thus still a vital means for establishing the wavelength ratios, and thus also the frequency ratios, of visible and near infrared stabilized lasers. As such, it complements the frequency-chain measurements that are now extending to visible frequencies. It will be interesting to see,
|
|
however, to what extent frequency techniques may re-
|
|
place the present role of wavelength measurement.
|
|
4. Interferometer Design
|
|
Wavelength measurements are carried out by interferometric comparison, using the optical length of the interferometer as a temporary or virtual intermediate reference. The interferometers that are used may be divided into two main classes:
|
|
(a) Low-finesse, usually with two-beam interference, such as the Michelson interferometer and its variants.
|
|
(b) High-finesse, with multiple-beam interference, of which the Fabry-Perot etalon is the normal form.
|
|
In their basic forms, both these systems form a Haidinger interference ring pattern in the image plane of an
|
|
extended source, the transmission maxima for a radiation of wavelength A. being given by:
|
|
m \ ^ 2t cos 8 ,
|
|
m where is the integer order of interference, t is the real
|
|
or effective separation of the reflecting surfaces, and 6 is the angle of incidence.
|
|
As illustrated in Fig. 1, the main difference between the two types of interferometer is the distribution of light in the pattern between the maxima. The two-beam system has a sinusoidal variation superposed on a constant background, whereas the multiple-beam system gives rise to a sharply peaked intensity distribution. It would seem that the multiple-beam system defines the intensity maxima more precisely and should thus be advantageous. In practice, however, this advantage is offset by other factors, such as transmission loss and asymmetry of the peaks due to maladjustment or optical defects.
|
|
Thus, both types of interferometer are roughly equally utihzed in precision measurement.
|
|
|
|
58
|
|
|
|
Two - beam
|
|
|
|
Curved mirrors are also used with Fabry-Perot etalons. With laser sources these take the form of modematched cavities, similar to laser cavities. Such cavities can be made long without i'equiring tiny pinholes, and they have a high finesse and transmission, giving excel-
|
|
lent sensitivity.
|
|
A further subdivision of interferometer designs is ac-
|
|
cording to the method of illumination:
|
|
|
|
(a) Spatially incoherent, or diffused laser light (b) Coherent laser beam.
|
|
|
|
Multiple -beam
|
|
6t
|
|
|
|
^
|
|
|
|
W2
|
|
|
|
61
|
|
|
|
Figure 1. Interferometers used for wavelength measurement. The two-beam (Michelson) form gives a sinusoidal intensity variation, the multiple-beam (Fabry-Perot) gives sharp intensity maxima.
|
|
Interferometer designs may also be divided into various sub-classes. One such sub-class is according to the
|
|
reflector shape:
|
|
|
|
(a) Flat reflectors
|
|
(b) Curved (spherical) reflectors.
|
|
|
|
Flat reflectors are the classical form which, as just
|
|
|
|
described, give rise to a Haidinger ring pattern. Meas-
|
|
urements can be made by measuring the diameters of
|
|
|
|
these rings, so that the fractional order at the centre
|
|
may be determined by extrapolation. This used to be the common measurement technique, but it is now rarely employed. More usually, as illustrated in Fig. 1, the central
|
|
portion of the interference pattern is isolated by transmission through a small hole, and measurements are made by varying the optical length in some linear or predictable manner. The angular size of the pinhole that
|
|
may be used depends inversely on the finesse and the re-
|
|
|
|
flector separation t. Thus, for example, with the 1-m
|
|
|
|
Fabry-Perot instrument at NPL, the optimum size of the
|
|
|
|
mm pinhole is only 0.1
|
|
|
|
radius for a focal length of 1 m.
|
|
|
|
This makes the instrument sensitive to focus imperfec-
|
|
|
|
tions and aberrations of the imaging system.
|
|
|
|
Curved mirrors in the form of adjustable cat's-eye re-
|
|
flectors are used in the two-beam interferometer at the
|
|
BNM in France [11]. This field-widened interferometer
|
|
enables a much larger detector pinhole to be used, which is particularly advantageous when using relatively weak
|
|
|
|
incoherent light sources such as the ^^Kr lamp. With
|
|
|
|
laser sources, the field-vddening technique enables
|
|
greater reflector separations to be contemplated than
|
|
BNM with flat mirrors, and it is planned to extend the
|
|
instrument to t = 2 m.
|
|
|
|
The forms of interferometer shown in Fig. 1 are designed for an incoherent source that has a uniform intensity over the area corresponding to the exit pinhole, and that
|
|
also radiates uniformly over a sufficient solid angle to fill the entrance lens. Laser beams do not provide such il-
|
|
lumination [12]. Partially coherent light, however, may
|
|
be formed with a diffuser. This gives rise to a speckle field, and quasi-uniform illumination is often achieved by moving or rotating this diffuser. Care must be taken, as illustrated in Fig. 2, to avoid a Doppler shift due to deviation of the light at the diffuser. Reversing the direction
|
|
of rotation reverses the shift, so that it may be measured
|
|
or cancelled.
|
|
|
|
Incident light Frequency I'
|
|
|
|
Moving diffuser velocity V
|
|
f (l + sin 0)
|
|
?^
|
|
|
|
Eg
|
|
Disc at 10 rev/s, with beam 50mm from rotation axis.
|
|
|
|
Doppler shift = 2x10""'°
|
|
|
|
for 6 = 1 degree.
|
|
|
|
Figure 2. Doppler shift from a moving ( or rotating) diffuser.
|
|
|
|
Coherent laser beams, however, are essential for the mode-matched form of interferometer. As showTi in Fig. 3, the equation specifying the exact length at which the transmission maxima occur is slightly different, and incorporates a phase shift term [13]. This term arises from the diffraction limited propagation of a laser beam [14]
|
|
and may have a magnitude of a significant fraction of a wavelength. Undiffused laser beams may also be used in two-beam interferometers. As shown in Fig. 4, the two
|
|
wavefronts that interfere have different radii of curvature and different diameters. The combined effect causes a slight reduction of visibility [15] together with a phase shift, which is additional, and of comparable magnitude,
|
|
to the propagation phase shift [16, 17, 18, 19].
|
|
|
|
59
|
|
|
|
Plane parallel Fabry -Perot (Incoherent illumination)
|
|
|
|
Mode - matched cavity (Laser illumination)
|
|
|
|
X = 2t Cos e
|
|
|
|
Radius R
|
|
0 X = 2t - X where © zCos-'(l -i- )'"
|
|
|
|
Figure 3. Resonance conditions (giving transmission maxima) for the plane-parallel Fabry-Perot etalon, and mode-matched cavity interferometers.
|
|
|
|
I
|
|
|
|
In addition to the propagation phase shift, there is a
|
|
|
|
phase shift due to the unequal wavefront curvatures
|
|
|
|
Combined effect:
|
|
|
|
~ —^— = D
|
|
|
|
arctan
|
|
|
|
7-
|
|
|
|
27r
|
|
|
|
2 TT Wo
|
|
|
|
Figure 4. Michelson interferometer with coherent laser illumination.
|
|
|
|
5. The Evolution of Wavelength Measurement Technique
|
|
|
|
During the last decade, the form of interferometer most
|
|
|
|
used for precision wavelength measurement has been the
|
|
|
|
pressure-scanned plane-mirror Fabry-Perot. With dif-
|
|
|
|
fused laser light, it is very suitable for measurements
|
|
|
|
directly with the
|
|
|
|
lamp. The use of the primary stand-
|
|
|
|
ard radiation, however, restricts the precision because its
|
|
|
|
bandwidth is wide and the etalon length must normally be
|
|
less than 20 cm. At the NPL [20, 21], the etalon was used
|
|
|
|
at near atmospheric pressure and scanned with a motor-
|
|
|
|
ized piston. By scanning alternately with pressure in-
|
|
|
|
creasing and decreasing, some effects of unequal elec-
|
|
|
|
tronic time delays could be eliminated, but scanning at
|
|
|
|
high pressure causes unfortunate temperature changes
|
|
|
|
and non-linearities. At the NBS (Gaithersburg) [22], the
|
|
|
|
NRML NRC (Canada) [23], and
|
|
|
|
(Tokyo) [24] the etalon
|
|
|
|
was placed in a vacuum chamber and scanned by leaking
|
|
|
|
dry nitrogen in through a supersonic nozzle. The interfer-
|
|
|
|
ence patterns are usually detected photoelectrically using chopped light, and digitized for computer analysis. At the
|
|
NRC, however, a moving photographic plate is used, and
|
|
this avoids the problems of unequal electronic delays. At
|
|
the IMGC (Italy) [25] the interferometer is kept evacu-
|
|
ated and the Haidinger ring image is scanned across an analysing slit in front of the photodector. The Fabry-
|
|
Perot of the NSL (Austraha) [26,27] is not usually
|
|
scanned, but is adjusted onto the interference maxima with a magnetic coil system that has a linear translation
|
|
characteristic and good reproducibility.
|
|
Michelson interferometer measurements of stabilized lasers relative to ^^Kr have also been carried out in
|
|
several laboratories. In the interferometers at BIPM [28] and PTB (West Germany) [17] the compensator plate may be tilted slightly so that the phase of the interfer-
|
|
ence pattern can be calculated by fitting a sinusoid to the intensities at four equispaced values of path difference.
|
|
The instrument at NPRL (South Africa) [29] has one mir-
|
|
ror on a parallel-spring translation member, driven by a
|
|
|
|
60
|
|
|
|
piezoelectric tube, with its position monitored by a ca-
|
|
|
|
pacitance transducer. The linearity and calibration of
|
|
|
|
this transducer are checked every time measurements are made. The observations are made by servolocking the
|
|
|
|
mirror to the positions corresponding to interference
|
|
|
|
maxima or minima and determining fringe fractions from
|
|
|
|
the capacitance transducer readings. With the field-
|
|
|
|
BNM widened instrument of the
|
|
|
|
(France) [11], one of the
|
|
|
|
cat's-eye reflectors may be moved on a parallel-spring
|
|
|
|
system by a differential screw together with a piezoelec-
|
|
tric element. It may be scanned continuously over a few
|
|
|
|
fringes, or servolocked to successive fringes of the refer-
|
|
|
|
ence laser. The measurement uncertainties in all these
|
|
|
|
measurements of stabilized lasers relative to ^^Kr is gen-
|
|
|
|
erally about 1 X 10~^ due to the practical limitations
|
|
|
|
imposed by the ^^Kr source, apart from the systematic
|
|
|
|
error in realizing the defined wavelength.
|
|
|
|
Significantly better accuracies are possible
|
|
in laser/laser comparisons. The path lengths may be
|
|
longer, and the source intensities are greater, so that
|
|
more powerful observational methods may be used. In my opinion the most important development in this field
|
|
has been the introduction of servolock methods, together
|
|
with tunable "slave" lasers. An early foretaste of this was the work of Bay, Luther, and White [30] shown in Fig. 5. Sidebands separated by ± w from the laser carrier v pass
|
|
through an optical isolator and the mode-matched cavity, and one servo-system locks the length of the cavity to the mean of the two fringe patterns, while the other modifies the frequency co so that the two sidebands resonate at the same cavity length. As well as pointing the way to servolock methods, the modulation technique used in this experiment is a useful way of estabhshing the approximate length, and hence the integer order number, of a long
|
|
interferometer [13, 31].
|
|
|
|
The use of a slave laser as the wavelength tunable element was introduced by Barger and Hall at the NBS, Boulder [32]. The slave laser is servolocked so as to give
|
|
a maximum transmission of the interferometer, and
|
|
|
|
—
|
|
hence an integer number of wavelengths, and its detuning from the stabilized laser is measured by the beat frequency. Their particular measurement was relative to ^Kr so that the accuracy of the result was modest. Their technique was, however followed at the NBS, Gaithersburg [13] in a measurement of the 3.39 |xm methane-stabilized He-Ne laser relative to the 633-nm iodine-stabilized laser. The reproducibility of these measurements was a few parts in 10^^, although the accuracy was limited to two parts in 10^'^ by systematic effects. The high precision of such measurements is due to the advantageous use that is made of the observation time, by comparison with scanning methods, and by the accu-
|
|
racy of beat frequency counting instead of fringe interpolation as the measurement procedure. Another advantage of the method is that because of the high precision, systematic effects, due for example to adjustment errors,
|
|
may be investigated quickly and without involving an undue amount of data gathering. The method is also used at
|
|
the PTB [34] and NPL [21, 33], and enables an accuracy
|
|
of a few parts in 10^^ to be achieved in visible laser comparisons [10].
|
|
Another wavelength measurement technique that has been developed in the last decade is that of fringecounting, in which a moving reflecting element is traversed over a significant fraction of a meter, while counting the interference fringes due to the unknown and a reference laser. Its advantage is that no prior approximate knowledge is needed of the unknown wavelength, or of a path difference. It is thus particularly suited to the swift determination of the wavelength output of tunable dye lasers to an accuracy of 1 x 10"*' or 1 x 10"^. As a precision measurement technique it is generally limited by alignment errors due to the use of cube-corner reflectors; but when designed with accuracy in mind, the tech-
|
|
nique may be as good as other two-beam interferometers. Thus with the MIT instrument [19] an accuracy of a few
|
|
parts in 10^^ should be possible.
|
|
The main limitations to accuracy in wavelength meas-
|
|
|
|
Modulalor
|
|
|
|
Isolator
|
|
|
|
Mode- matched
|
|
|
|
10 GHz
|
|
|
|
—A<+B
|
|
PSD A-B vco
|
|
|
|
Counter
|
|
Figure 5. The apparatus of Bay, Luther, and White (1972), usnig a servo-locked modematched cavity interferometer, with feedback tuning of the source so that both sidebands (v -\- u)) and (v — (ji) resonated simultaneously.
|
|
61
|
|
|
|
urement are:
|
|
|
|
(a) Flatness errors (or non-uniformity of curvature) of surfaces,
|
|
(b) Non-uniformity of illumination (or mode impur-
|
|
ity),
|
|
(c) Defects of imaging (or mode matching),
|
|
(d) Non-linearity of interpolation, (e) Diffraction effects, (f) Prismatic dispersion of windows, (g) Parallelism and alignment errors, (h) Electronic imperfections.
|
|
|
|
The flatness or errors of figure are the most serious
|
|
|
|
A problem.
|
|
|
|
1-m interferometer is roughly 3 x 10^ half-
|
|
|
|
wavelengths in length, so that to achieve an accuracy of
|
|
|
|
3 X 10" each interference fringe must be subdivided to
|
|
|
|
10"^ of the fringe separation. The flatness of optical sur-
|
|
|
|
faces is seldom better than X./100. The extra accuracy is
|
|
|
|
achieved by averaging over the irregularities. The prob-
|
|
|
|
lem is to get the same average with both the radiations
|
|
|
|
being compared, and this is a particularly serious prob-
|
|
|
|
lem with interferometers that use spatially coherent
|
|
|
|
light, as the illuminated area then depends upon the
|
|
|
|
wavelength.
|
|
|
|
6. Wavelength Results
|
|
|
|
Many precision wavelength measurements have been carried out on the methane- and iodine-stabilized He-Ne laser radiations at 3.39 |xm and 633 nm, a few on the COo
|
|
laser system, and a few also on other iodine-stabilized visible radiations. Measurements of the 633-nm laser, relative to ^''Kr have been reported by 10 laboratories, using a variety of interferometer designs. As mentioned above, the measurement uncertainties are generally in the region of 1 x 10"^, and their agreement well within 4 x 10"^. Measurements of the 3.39 [xm radiation directly with respect to ^^Kr, reported by four laboratories, have a slightly worse measurement uncertainty of about 4 x 10"^
|
|
|
|
The ratio of the two wavelengths 3.39 |jLm/0.633 fxm has
|
|
|
|
also been determined interferometrically. Direct meas-
|
|
|
|
urements suffer the problem of the large diffraction ef-
|
|
|
|
NBS fect for the infrared radiation. In the
|
|
|
|
(Gaithers-
|
|
|
|
burg) measurement [13] this limited the accuracy to 2 x
|
|
10""^. A measurement at the PTB [34], however, was
|
|
|
|
limited to an uncertainty of 2 x 10 as also was a meas-
|
|
|
|
urement at the NPL.
|
|
|
|
A measurement by the NRC [34] avoided this difficulty
|
|
|
|
by mixing the infrared radiation with that from a 633-nm
|
|
|
|
laser in a non-Hnear crystal, so as to give sum-frequency
|
|
|
|
radiation in the green. From a wavelength measurement
|
|
|
|
of this green light relative to a 633-nm iodine standard,
|
|
|
|
the required 3.39/0.633 ratio was determined. By this
|
|
|
|
method the severe diffraction problem is avoided; but the
|
|
|
|
penalty is that the uncertainty of measurement is multi-
|
|
|
|
plied by the wavelength ratio in calculating the infrared
|
|
|
|
wavelength. Thus the uncertainty of the infrared /visible
|
|
|
|
ratio was 7 x 10"^.
|
|
|
|
This non-linear optical mixing method has also been used to measure the wavelength ratio of a 9.7 |xm CO2 laser to the 633-nm laser, in this case by generating the
|
|
difference frequency in the deep red end of the visible
|
|
spectrum. A measurement at the NPL by a pressure
|
|
scanning method [21] had an uncertainty of 5 x 10"^.
|
|
Subsequently with a servolock flat-plate Fabry-Perot system an uncertainty of 4 x 10"^" was achieved for the
|
|
|
|
A infrared /visible ratio [10]. direct measurement of the
|
|
CO2 wavelength is subject to serious limitation by diffraction. Thus for the MIT measurement [19], the diffraction correction was -2 x 10"^ with a ±20% uncer-
|
|
tainty, corresponding to an uncertainty in the wavelength ratio of 4 x 10"^ and making the total wavelength ratio uncertainty 6 x 10~^.
|
|
|
|
Only a few visible /visible laser wavelength ratios have
|
|
|
|
been measured precisely. The ratio of the iodine-stabi-
|
|
|
|
lized Ar^ laser radiation to the 633-nm laser has been
|
|
|
|
measured with an uncertainty of 4 x 10"^" at the BIPM
|
|
|
|
[35] and by a servolock two-beam method at the PTB
|
|
|
|
BNM [34], with an uncertainty of 5 x lO'^"^. The
|
|
|
|
have
|
|
|
|
also made a measurement [36], with an uncertainty 3 x 2Q-io_ rpj^g 612-nm iodine-stabilized He-Ne laser has been
|
|
|
|
measured with respect to the 633-nm laser by the BIPM
|
|
|
|
with an uncertainty of 3 x lO"^'' [35].
|
|
|
|
These results, however, do not represent the limit of
|
|
|
|
what may be achieved by existing techniques. With the
|
|
|
|
MIT system it is suggested that with visible radiations,
|
|
|
|
where diffraction is less important, the measurement un-
|
|
|
|
certainty would be reduced to a few parts in 10". The
|
|
BNM instrument is also believed to be capable of similar
|
|
|
|
accuracy [37], and a redesigned PTB instrument is being
|
|
|
|
considered that would also give performance to this
|
|
level. The C02/visible measurement at the NPL [10] in-
|
|
|
|
volved a visible /visible wavelength ratio determination
|
|
|
|
vdth
|
|
|
|
an uncertainty
|
|
|
|
of 3
|
|
|
|
x
|
|
|
|
10"^ .
|
|
|
|
It is
|
|
|
|
thus realistic
|
|
|
|
to
|
|
|
|
quote 3 x 10"" as the level of performance that may be
|
|
|
|
achieved for visible laser radiations by current methods
|
|
|
|
of interferometric wavelength measurement.
|
|
|
|
The present wavelength standards shown in Table 1 have their uncertainties set by the 4 x 10"^ figure associated with the ^^Kr standard. If it were not for this limit.
|
|
|
|
Table 1. Reference standards for length measurements.
|
|
|
|
^^Kr, transition 2p iq - 5^5, c, the speed of light
|
|
|
|
wavelength 605 780 211 fm 299 792 458 m/s
|
|
|
|
Laser Absorber Transition
|
|
|
|
Component Wavelength, fm
|
|
|
|
He-Ne He-Ne He-Ne
|
|
Ar+
|
|
|
|
CH4
|
|
127i,
|
|
|
|
V3
|
|
|
|
P(^)
|
|
|
|
;
|
|
|
|
11-5 i2(127) ;
|
|
|
|
9-2 i2(47) ;
|
|
|
|
43-0 P(13)' ;
|
|
|
|
FP
|
|
i
|
|
;
|
|
0
|
|
;
|
|
; as
|
|
|
|
3 392 231 400 632 991 399 611 970 771 513 673 467
|
|
|
|
"All have identical uncertainties of 4 parts in 10^.
|
|
the uncertainties of the laser standards would now be a
|
|
factor of 10 better, with prospects for a further factor of 10 improvement. There is thus pressure to change the definition of the meter so as to avoid this limitation to ac-
|
|
curacy. The discussion on this has been active during the past decade, and action is now imminent. The proposed redefinition is such that the speed of light will become a
|
|
fixed constant with the value given in 1973 (299 792 458 m/s). This value was determined from frequency and wavelength measurements of the 3.39 |xm methane-stabi-
|
|
lized laser (c = / X), with an uncertainty that reflects
|
|
A essentially only the ^''Kr uncertainty of realization.
|
|
number of different formulations have been suggested for the wording of the new meter definition [38, 39, 40].
|
|
After a joint CCDM/CCU discussion in April 1981, how-
|
|
ever, only two alternatives remain, with the bulk of opin-
|
|
|
|
62
|
|
|
|
ion being in favor of:
|
|
|
|
(a) "The meter is the length equal to the distance travelled by plane electromagnetic waves in free
|
|
space in a time interval of 1/299 792 458 of a second."
|
|
|
|
The alternative is:
|
|
|
|
(b) "The meter is the length equal to //299 792 458
|
|
wavelengths in free space of plane electromagnetic waves of which the frequency, expressed in hertz, has the numerical value /."
|
|
|
|
The majority of people prefer wording (a) as it is easier to understand, being simpler and more elegant in con-
|
|
A cept. minority of metrologists prefer wording (b) be-
|
|
cause it is closer to the means of realization of 1-m lengths by means of laser wavelength standards. It is most hkely, however, that wording (a) will prevail.
|
|
A redefinition of the meter in this form may be recom-
|
|
mended in 1982, for formal adoption in 1983 by the Gen-
|
|
eral Conference of Weights and Measures. When this
|
|
takes place, the uncertainties of the stabilized laser wavelengths will have to be revised, and so will their numerical values. Present evidence suggests that the 3.39
|
|
|jLm wavelength will be reduced by 3 fm, and the three visible laser values will each be reduced by about 1 fm, with an extra digit being added after the decimal point, as the uncertainties improve by a factor of 10.
|
|
|
|
7. Length Measurement
|
|
|
|
In interferometric wavelength comparison, the me-
|
|
|
|
chanical length of the interferometer is a kind of inter-
|
|
mediate standard. It is effectively "measured" by the
|
|
|
|
standard radiation, although its length is not actually cal-
|
|
culated. An analogous case is the Michelson-Morley type
|
|
|
|
of experiment carried out by Brillet and Hall [41] in which the length of a 30-cm mode-matched cavity was
|
|
|
|
monitored by reference to a 3.39 |xm methane-stabilized laser. The cavity length drifted at a rate of about 5 x 10"^^ /s and distorted by ±1 x 10"^- by gravitational
|
|
stretching as it was rotated. By averaging over many days, however, it was possible to show that its optical length was independent of its orientation in inertial space
|
|
to an uncertainty of 2.5 x 10"^"^. This is metrology of ex-
|
|
treme precision.
|
|
|
|
Even better precision is sought in interferometer systems designed to detect gravitational waves. The first such system was built and operated at the Hughes
|
|
|
|
Research Laboratories in Malibu, California, in the early
|
|
|
|
1970' s [42]. This instrument had folded arms of effective
|
|
|
|
m length 4.25
|
|
|
|
and had a strain resolution of 10"^^
|
|
|
|
(Hz)"^, so that it would have been capable of detecting gravitational waves that gave a total strain level of 10~
|
|
over the audio band (1 to 20 kHz). Now several gi'oups
|
|
around the world are developing interferometers of
|
|
|
|
greatly improved sensitivity. At the California Institute
|
|
of Technology, for example, the aim is to build an inter-
|
|
m ferometer with a baseline of 40 so as to detect strains
|
|
of about 3 X 10"^^ on miUisecond timescales. A long term
|
|
|
|
goal is to construct large scale systems, with baselines of about 1 km, in order to achieve a strain sensitivity of
|
|
10"^^^ for frequencies from about 30 Hz to 10 kHz. Such sensitivity would match the estimated strength of gravitational waves that should occur reasonably often. Apart from the mechanical problems, such measurements must be limited by (a) the detection statistics (photon-counting error), which means that high-power lasers should be
|
|
|
|
used, and (b) the disturbance to the momentum, and
|
|
hence the subsequent position of the reflecting mirrors,
|
|
by radiation pressure fluctuations. An interesting discus-
|
|
sion has been taking place on this latter aspect [43], regarding details of its applicability, and whether or not
|
|
some arrangement may be devised to reduce its effect.
|
|
If interferometers are rigidly connected to the ground,
|
|
then they measure earth strain. A number of such instru-
|
|
ments have been developed around the world for geophysical studies. The motion of the earth's surface behaves like a stochastic process, with the notable exception of earthquakes and earth tides. This strain noise spectrum [44] seems to be similar at different sites, and forms the limitation to observations. Against this background, the
|
|
normal modes of oscillation of the earth may readily be measured after an earthquake, and earth tides studied in
|
|
detail and correlated with the local geology and topography [45].
|
|
Distances of kilometer dimensions measured in the earth's surface by optical means are limited in accuracy by the refractivity of the earth's atmosphere. This is of magnitude 3 x lO"'', so that to get an accuracy of 10"' an accurate correction must be applied. The use of two optical wavelengths allows partial cancellation, but the water vapor still presents some problem. The addition of a radio-frequency measurement should be a great improve-
|
|
A ment. three-wavelength instrument of this kind being developed in NBS Boulder [46] is aimed at a measure-
|
|
ment accuracy of 5 x 10"* over a 50 km range. This is,
|
|
incidentally, similar to the relative accuracy achieved for 1-m length bars measured by interferometry.
|
|
Over the larger distances in space beyond the earth's atmosphere, refractive index is no longer a problem. After a decade of observations at the McDonald Observatory, lunar ranging has provided a lot of information about the orbital dynamics of the earth-moon system [47, 48]. The fitting of this data to the various models of the orbits, rotations, etc. is a complex task. As a length measurement project, the problems are formidable. Nevertheless, a range precision of 4 x lO"-'"^ is achieved; a remarkable achievement on a moving target at which 10^^ photons are transmitted, but only one comes back 2.5 seconds later. It should be possible to use lunar ranging results made at two different earth stations to measure the secular variation of the distance between them. Data gathered over 10 years could determine this parameter to an accuracy of 1 cm/year.
|
|
Even higher relative accuracy has been achieved in the radio ranging experiments made for the Viking relativity experiment [49, 50]. Two Viking landers implanted on
|
|
the surface of Mars, and orbiting spacecraft, echoed modulated microwave signals back to earth with a round trip of 2500 seconds. The total time uncertainty of 10 ns, in favorable circumstances, corresponds to a fractional precision of 4 x 10"^- in the distance to Mars.
|
|
The proposed redefinition of the meter will allow such precise measurements to be expressed absolutely in meters instead of only in time delay, and it will thus benefit astronomers, as well as all who are concerned with precise laboratory measurements and stabilized lasers.
|
|
References
|
|
[1] Report of the Advisory Committee for the Definition of the
|
|
M Meter, 1979, Appendix 3, pp. M46-M55. (Bm-eau Inter-
|
|
national des Poids et Mesures, F92310 Se\Tes, France,
|
|
1979).
|
|
[2] R. L. Bai-ger and J. L. Hall, Phvs. Rev. Lett. 22. 4 (1969). [3] G. R. Hanes and K. M. Baird, Metrologia 5, 32 (1969).
|
|
|
|
63
|
|
|
|
[4] Report of the Advisory Committee for the Definition of the Meter, 1973. Recommendation M2. (Bureau International
|
|
|
|
des Poids et Mesui-es, F92310 Sevres, France, 1979).
|
|
|
|
[5] Report of the Advisory Committee for the Definition of the Meter, 1979. Appendix M2-C, pp. M31-M45. (Bureau International des Poids et Mesures, F92310 Sevres,
|
|
|
|
France, 1979).
|
|
|
|
MOM [6] B. R. Marx and W. R. C. Rowlev, NPL Report
|
|
|
|
51,
|
|
|
|
April 1981.
|
|
|
|
[7] W. R. C. Rowley and B. R. Marx, Metrologia 17, 65 (1981).
|
|
[8] F. Spieweck, IEEE Ti-ans. Instrum. Meas. IM-29, 361
|
|
|
|
(1980).
|
|
[9] P. Cerez, A. Brillet, C. N. Man-Pichet, and R. Felder,
|
|
IEEE Trans. Instrum. Meas. IM-29, 352 (1980). [10] P. T. Woods, K. C. Shotton, and W. R. C. Rowley, Appl.
|
|
|
|
Opt. 17, 1048 (1978).
|
|
[11] P. Bouchareine, Bulletin BNM, No. 24, 3, (1976).
|
|
[12] D. A. Solomakha, Meas. Tech. 16, 1167, (1973).
|
|
[13] H. P. Layer, R. D. Deslattes, and W. G. Schweitzer, Jr.,
|
|
|
|
Appl. Opt. 15, 734 (1976). [14] H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
|
|
[15] W. R. C. Rowley, Opt. Acta 16, 159 (1969). [16] F. Bayer-Helms, PTB-Bericht Me-16 (Physikalisch-
|
|
Technische Bundesanstalt, January 1977).
|
|
|
|
[17] G. Bbnsch, PTB-Bericht Me-17 (Physikalisch-Technische
|
|
Bundesanstalt, May 1977).
|
|
|
|
[18] K. Dorenwendt and G. Bbnsch, Metrologia 12, 57 (1976). [19] J. -P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit,
|
|
|
|
A. Szoke, F. Zernike, P. H. Lee, and A. Javan, Appl. Opt.
|
|
|
|
20, 736 (1981).
|
|
[20] W. R. C. Rowley and A. J. Wallard, J. Phys. E. 6, 647
|
|
|
|
(1973).
|
|
|
|
[21] T. G. Blaney, C. C. Bradley, G. J. Edwards, D. J. E. Knight, W. R. C. Rowley, K. C. Shotton, and P. T.
|
|
|
|
Woods, Proc. R. Soc. London Ser. A: 355, 89 (1977). [22] W. G. Schweitzer, Jr., E. G. Kessler, Jr., R. D. Deslattes,
|
|
|
|
H. P. Layer, and J. R. Whetstone, Appl. Opt. 12, 2927
|
|
|
|
(1973).
|
|
|
|
[23] G. R. Hanes, K. M. Baird, and J. DeRemigis, Appl. Opt. 12,
|
|
|
|
1600 (1973).
|
|
|
|
[24] N. Ito and K. Tanaka, Metrologia 14, 47 (1978). [25] F. Bertinetto and A. Sacconi, in Atomic Masses and Funda-
|
|
mental Constants 5, Ed. by J. H. Sanders and A. H.
|
|
Wapstra (Plenum Press, New York, 1976), p. 357.
|
|
[26] J. B. Cole and C. F. Bruce, Appl. Opt. 14, 1303 (1975). [27] C. F. Bruce and R. M. Duffy, Rev. Sci. Instrum. 46, 379
|
|
|
|
(1975).
|
|
|
|
[28] A. J. Wallard, J. M. Chartier, and J. Hamon, Metrologia 11,
|
|
|
|
89 (1975).
|
|
|
|
[29] F. H. Mliller and R. Turner, J. Phys. E: Sci. Instrum. 13, 1024 (1980).
|
|
[30] Z. Bay, G. G. Luther, and J. A. White, Phys. Rev. Lett. 29, 189 (1972).
|
|
[31] F. Bien, M. Camac, H. J. Caulfield, and S. Ezekiel, Appl. Opt. 20, 400 (1981).
|
|
[32] R. L. Barger and J. L. Hall, Appl. Phys. Lett. 22, 196
|
|
(1973).
|
|
[33] W. R. C. Rowley, K. C. Shotton, and P. T. Woods, in Atomic Masses and Fuyidameyital Constants 5, Ed. by J.
|
|
H. Sanders and A. H. Wapstra (Plenum Press, New York,
|
|
1976), p. 410.
|
|
[34] G. Bbnsch, Document CCDM/79-20, submitted to the Advisory Committee for the Definition of the Meter, 1979. (Bureau International des Poids et Mesures, F92310
|
|
Sevres, France, 1979).
|
|
[35] Document CCDM/79-12, submitted to the Advisory Committee for the Definition of the Meter, 1979. (Bureau International des Poids et Mesures, F92310 Sevres, France, 1979).
|
|
[36] P. Bouchareine and B. Rougie, Document CCDM/79-18, submitted to the Advisory Committee for the Definition of the Meter, 1979. (Bureau International des Poids et Mesures, F92310 Sevres, France, 1979).
|
|
[37] P. Bouchareine, Bulletin BNM, No. 43, 9, (1981). [38] Document GT-M.U./N° 2. submitted to the CCDM/CCU
|
|
working group on the Definition of the Meter, April 1981. (Bureau International des Poids et Mesures, F92310 Sevres, France, 1981). [39] D. T. Goldman, J. Opt. Soc. Am. 70, 1640 (1980).
|
|
[40] P. Bouchareine, Bulletin BNM, No. 43, 12, (1981).
|
|
[41] A. Brillet and J. L. Hall, Phys. Rev. Lett. 42, 549 (1979).
|
|
[42] R. L. Forward, Phys. Rev. D 17, 379 (1978).
|
|
[43] B. R. Marx, Nature (London) 287, 276 (1980). [44] J. Berger and J. Levine, J. Geophys. Res. 79, 1210 (1974). [45] J. Levine and J. C. Harrison, J. Geophys. Res. 81, 2543
|
|
(1976).
|
|
[46] S. E. Moody and J. Levine, Tectonophys. 52, 77 (1979). [47] Yu. L. Kokurin, Sov. J. Quantum Electron. 6, 645 (1976).
|
|
[48] J. D. Mulholland, Rev. Geophys. Space Phys. 18, 549 (1980). [49] I. I. Shapiro, R. D. Reasenberg, P. E. MacNeil, R. B. Gold-
|
|
stein, J. P. Brenkle, D. L. Cain, T. Komarek, A. I. Zygielbaum, W. F. Cuddihy, and W. H. Michael, Jr., J. Geophys. Res. 82, 4329 (1977). [50] R. D. Reasenberg, I. I. Shapiro, P. E. MacNeil, R. B. Goldstein, J. C. Briedenthal, J. P. Brenkle, D. L. Cain, T. M. Kaufrnan, T. A. Komarek, and A. I. Zygielbaum, Astrophys. J. 234, L219 (1979).
|
|
|
|
64
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Double-Mode Method of Sub-Doppler Spectroscopy and Its Application in Laser Frequency Stabilization
|
|
N. G. Basov, M. A. Gubin, V. V. Nikitin, A. V. Nikulchin, and D. A. Tyruikov
|
|
|
|
P. N. Lebedev Physical Institute, U.S.S.R., Moscow, 117924 and
|
|
|
|
V. N. Petrovskiy and E. D. Protscenko Institute of Physical Engineering, U.S.S.R., Moscow, 115409
|
|
|
|
We present some results of the investigation of the proposed high sensitivity method of sub-
|
|
|
|
Doppler spectroscopy and laser frequency stabilization which is based on the parameters of a double-
|
|
|
|
DM A mode (DM) gas laser containing an internal absorption cell. short
|
|
|
|
He-Ne/CH4 laser was con-
|
|
|
|
structed which has relative frequency stability better than 10"^'^ and radiation spectral width < 10 Hz.
|
|
|
|
DM When a telescopic beam expander was used inside the cavity of the short
|
|
|
|
He-Ne/CH4 laser, super-
|
|
|
|
narrow reference spectral lines of about 3 kHz in width were obtained, and the magnetic hyperfine
|
|
|
|
structure (hfs) of the F,-' methane line was resolved.
|
|
|
|
Key words: double-mode method; He-Ne laser; methane cell; sub-Doppler spectroscopy.
|
|
|
|
1. Introduction
|
|
|
|
The recent development of optical frecjuency standards is based on obtaining super-narrow spectral lines with nonlinear sub-Doppler laser spectroscopy methods. Extremely small values of collision, saturation, and transit
|
|
|
|
flight time broadening are required for obtaining spectral
|
|
lines of 10"- 10'^ Hz in width. In particular, if one uses the method of inverted Lamb-dip with an internal or external absorption cell, very low gas pressures and weak optical fields are needed. An essential difficulty in experimentally obtaining such narrow resonances is the rapid decrease of the signal-to-noise ratio when low absorption gas pressures of 0. 1 to 1 mPa are used.
|
|
|
|
The present paper reports the results of studying the
|
|
|
|
double-mode method of sub-Doppler spectroscopy, which
|
|
|
|
has much higher sensitivity for obtaining narrow reso-
|
|
|
|
nances in a laser with an internal absorption cell as com-
|
|
|
|
pared to single mode laser operation. The investigations
|
|
|
|
have been carried out with a double-mode He-Ne /CH4
|
|
|
|
laser (at wavelength K = 3.39 [xm,
|
|
|
|
line of methane),
|
|
|
|
which attracts attention as a possible high accuracy opti-
|
|
|
|
cal frequency standard [1].
|
|
|
|
Stable double-mode operation of the laser is realized with the help of a Fabry-Perot cavity, containing two quarter wave plates [2]. The laser provides stable operation near the gain curve center on the two adjacent axial modes possessing orthogonal linear polarizations.
|
|
|
|
In contrast to a single-mode laser (SML) two types of narrow resonances, "amplitude" and "frequency" (which possess a number of advantages) can be observed in the double-mode laser (DML) radiation (Fig. 1).
|
|
|
|
2. Amplitude Resonances of the DML
|
|
|
|
In the observation of the output power of a separate mode there appear "amplitude" resonances (AR) (Fig. 2)
|
|
which are similar to the inverted Lam.b-dip, but may be
|
|
|
|
DOUBLE- MODE LASER
|
|
|
|
^^^^^^^^ polarizer
|
|
|
|
^// [h?n3 [ch] //
|
|
|
|
„5L0W" /4FC
|
|
SY5TEM
|
|
|
|
AR
|
|
REGISTRATION
|
|
|
|
.FAST" AFC
|
|
SYSTEM
|
|
|
|
ER
|
|
REGISTRATION
|
|
|
|
E*E2 cos tOfst
|
|
|
|
Figure 1. The scheme of the AR and FR observation in the
|
|
|
|
AR DML. With respect to polarizer position,
|
|
|
|
FR (1),
|
|
|
|
(3), or
|
|
|
|
both resonances simultaneously (2) may be observed. In posi-
|
|
|
|
tion (2) the resonances are used as discriminators for the two-
|
|
loop AFC systems.
|
|
|
|
about two orders of magnitude higher than the SML
|
|
|
|
resonances. Such a sharp increase in the sensitivity is
|
|
|
|
reached by creating a strong interaction regime between
|
|
|
|
orthogonally polarized modes. The ratio between reso-
|
|
|
|
DML nance amplitude (a _) in SML and
|
|
|
|
is as follows:
|
|
|
|
a - (SML)
|
|
|
|
a -(DML)
|
|
|
|
(1)
|
|
|
|
./ int
|
|
|
|
where /int = 10 ^ - 10 - is the mode interaction parame-
|
|
ter [2].
|
|
|
|
The physical mechanism of the sharp increase in the
|
|
|
|
AR DML in the
|
|
|
|
consists in the following: when the fre-
|
|
|
|
quencies of the two modes (wi, mo) are scanned their intensities can be made approximately equal. If, for example, the first mode frequency wi coincides with the
|
|
|
|
65
|
|
|
|
Figure 2. The a mplitude of resonances of the DML. Ei is the in-
|
|
|
|
DML tensity of one of the two }nodes; Ei the total
|
|
|
|
intensity;
|
|
|
|
p. = iOO mPa, 7_ = 150 kHz.
|
|
|
|
center of an inhomogeneously broadened absorption line
|
|
(wi ^ (si-), the mode losses change slightly due to the for-
|
|
mation of the Lamb-dip. For weakly absorbing or poorly saturated transitions in molecular gases at low pressures,
|
|
the change in losses is usually about 0.1% and may be an order of magnitude smaller. Approximately the same con-
|
|
trast of narrow inverted Lamb-dip resonances is ob-
|
|
served in SML operation. But in DML operation the strong coupling between the
|
|
modes leads to a sharp intensity re-distribution among the modes. It is possible to realize the situation when ap-
|
|
proximately all the active atoms radiate in the first mode.
|
|
AR contrast may constitute 30-40% of the total laser
|
|
power even in the case of a short laser. When the length of the He-Ne cavity ('o is 60-80 cm, the transverse size of the mode distribution, f/_, in the cell about 2 mm, and
|
|
the methane pressure p _ within the range of
|
|
(0.2-0.7) Pa, the AR width y- is equal to 100-150 kHz. Under these conditions a large value of AR and high S/N
|
|
ratio allowed us to obtain a laser frequency stability of
|
|
better than 10"^^ (Allan variance for t = 10 sec averaging
|
|
time).
|
|
Increase of the AR by changing the mode interaction
|
|
(decreasing /int) is limited by two factors: the increase in natural laser intensity noise and instability of the double-mode regime.
|
|
3. Frequency Resonances of the DML
|
|
|
|
The frequency resonances (FR) of the DML are ob-
|
|
|
|
served as changes in the beat frequency between modes
|
|
|
|
and are caused by resonant changes in the Doppler-
|
|
|
|
broadened dispersion line of the absorption medium
|
|
|
|
under the influence of standing wave field saturation
|
|
|
|
DML (frequency pulling to the line center [3]). In the
|
|
|
|
with an internal absorption cell the frequency spacing
|
|
|
|
» between modes coi2 =0)1-0)9 changes in the following
|
|
|
|
way (with
|
|
|
|
- |o)i
|
|
|
|
o)_
|
|
|
|
~ -y_;
|
|
|
|
7-):
|
|
|
|
|
|
|
|
|
+ ~ = 0)12
|
|
|
|
cof.
|
|
|
|
Aa)io
|
|
|
|
+ o)ll
|
|
|
|
lo
|
|
|
|
~
|
|
|
|
J-^^' 7- + (o)i
|
|
|
|
-
|
|
|
|
.^(2)
|
|
o)_)-
|
|
|
|
where a_ is the nonsaturated absorption coefficient per
|
|
|
|
unit length; c is the speed of light; and
|
|
|
|
is the normal-
|
|
|
|
ized intensity of the mode which coincides with o)„.
|
|
In our experiments with the He-Ne /CH4 DML contain-
|
|
ing two \/4 plates the beat frequency 0)12 was determined for the range (2-5) MHz, and its change (A 0)12) was
|
|
~ 10^ Hz, when p_ = (0.2 - 0.4) Pa and L'. ~ 0.5 m.
|
|
|
|
FR Reference [4] describes the first observation of
|
|
|
|
in
|
|
|
|
DML the
|
|
|
|
with an absorption cell. FR in the SML has also
|
|
|
|
been studied [5, 6] with the use of an additional hetero-
|
|
|
|
DML dyne laser. In the
|
|
|
|
the heterodyne function is per-
|
|
|
|
formed by the second mode.
|
|
|
|
3.1 Increasing DML Short-Term Frequency Stability
|
|
|
|
One of the requirements for obtaining super-narrow spectral lines with 7- ~ 10^ Hz is high short-term fre-
|
|
quency stability of the laser. The laser spectral width (Ao)s) must be considerably less than the resonance width 7- . It is well known that the frequency spectrum narrow-
|
|
ing in any type of laser used in precision spectroscopy is
|
|
accomplished by means of frequency stabilization with a
|
|
broad-band automatic frequency control (AFC) system. The best results in He-Ne /CH4 laser spectrum narrowing
|
|
have been achieved by Chebotayev et al. [7]. They obtained a spectral width A o)s ~ 1 Hz when using intense
|
|
(a _ ~ 1 mW) and narrow (7- ~ 50 kHz) resonances in a 5-
|
|
meter length laser.
|
|
|
|
In the present paper we suggest another method of
|
|
laser spectrum narrowing. The main idea is that the laser
|
|
frequency be stabilized to the reference line by a two-
|
|
loop AFC system, using different molecular frequency discriminators (Fig. 1). The first AFC reduces "slow"
|
|
frequency fluctuations in the range 0-10 Hz and uses as
|
|
a reference point the top of the AR. This is the com-
|
|
monly used AFC where laser frequency changes are detected as intensity changes. The second AFC reduces
|
|
"fast" fluctuations with a frequency of more than 10 Hz.
|
|
The FR of the DML is used as a frequency discriminator
|
|
for this AFC.
|
|
|
|
Note the main advantages of such a combined system:
|
|
|
|
the "fast" feedback loop does not need laser cavity modu-
|
|
lation and, consequently, the AFC band (A/afc) is limited
|
|
only by 7-, not by the modulation frequency, and may be,
|
|
|
|
therefore, 5-10 times wider than in ordinary AFC. As the
|
|
|
|
amplitude detection is replaced by frequency detection, so
|
|
|
|
AR the demands on
|
|
|
|
intensity are considerably less. At
|
|
|
|
the same time the value of FR(A 0)12) is proportional only
|
|
to a linear absorption and hence, weakly depends on AR
|
|
contrast. Therefore one can obtain for short lasers a FR of ~ 10'^ Hz in magnitude.
|
|
|
|
Figure 3b shows gain-frequency dependences of the
|
|
constructed ARC, which has frequency band width A/afc = 20 kHz.
|
|
|
|
Figure 3a shows the mode beat signal, observed on a
|
|
spectrum analyzer screen with the DML frequency stabil-
|
|
|
|
ized by the double AFC. The full width at half maximum (FWHM) of the observed signal corresponds to the laser
|
|
|
|
frequency spectrum, multiplied by the derivative
|
|
|
|
d (x)i/d 0)12 in the center of the absorption lines. For our
|
|
|
|
experimental conditions the value of d oji/d 0)12 varied
|
|
|
|
within the range 5-1.2. Taking into account the value
|
|
|
|
of d uii/d o)i2 the measurements gave the stabilized laser frequency spectrum A < ojg'^' 10 Hz. The passive laser
|
|
|
|
frequency spectrum was about 8 kHz. The main contribu-
|
|
|
|
tion to the Ao)!*^' was made by the fluctuations of a
|
|
radiogenerator used in the AFC frequency-to-voltage
|
|
|
|
DML converter. Other parameters of the
|
|
|
|
are as follows:
|
|
|
|
We t'o = 1.5 m, ('- = 0.8 m, d = 2.10-3m, p_ = 0.3 Pa.
|
|
|
|
66
|
|
|
|
fASV'AfC
|
|
|
|
DML Figure 3. a) The mode beat frequency spectrum of the
|
|
|
|
AFC stabilized with the two-loop
|
|
|
|
system, b) The gain-
|
|
|
|
frequency dependence of the "slow" and 'fast" AFC parts. The
|
|
|
|
unity gain is at 20 kHz.
|
|
|
|
hope that further development of the method would allow one to obtain the natural laser spectral width.
|
|
|
|
3.2 Sensitivity of FR Registration in DI\/IL
|
|
|
|
The investigation of the FR shows that frequency detec-
|
|
|
|
DML tion of resonances in the
|
|
|
|
may be more sensitive in
|
|
|
|
comparison with AR and FR registration in the SML. This
|
|
|
|
DML feature of the
|
|
|
|
FR is especially important for super-
|
|
|
|
narrow reference line detection (7- < 1 kHz) with low
|
|
|
|
pressures of the absorption gas (p - =1-10 mPa).
|
|
|
|
Three noise sources must be taken into account for the
|
|
FR detection: additive noise, F/V transformation noise,
|
|
|
|
and natural frequency noise of the radiation. Using well
|
|
known relations [8] we may show that for additive noise the S/N ratio (by voltage) for the frequency detection is essentially more than for the amplitude detection:
|
|
|
|
(S/N)kr
|
|
|
|
E E \
|
|
|
|
2
|
|
|
|
(3)
|
|
|
|
(S/N) AR add
|
|
|
|
fm
|
|
|
|
E E where i, 2 are electric fields of the modes; / „, is the
|
|
modulation frequency (synchronous detection i.s sup-
|
|
posed); 0 - is the value of AR in SML or in DML; and
|
|
A 0)12 is defined by Eq. (2).
|
|
The ci-IEiEo ratio is equal approximately to the AR
|
|
contrast. Equation (3) shows that when ~ /„, 10" Hz, a-/EiE2-~ 10"\ A 0)12 ~ 10'' Hz the gain in the S/N ratio may be a few orders of magnitude. In practice the fre-
|
|
quency characteristics of the photodetector must be
|
|
|
|
taken into account in addition to (3).
|
|
|
|
As to the F/V transformation noise the main contribu-
|
|
|
|
tion to its spectral density is made in the optical hetero-
|
|
dyne process. In the DML the second mode is used as the
|
|
|
|
internal local oscillator and its frequency technical fluc-
|
|
|
|
tuations are strongly correlated with the first mode's
|
|
|
|
« fluctuations if the following condition is realized: -7-
|
|
|
|
« A 0)12
|
|
|
|
7+,
|
|
|
|
(7+ is the gain line homogeneous width,
|
|
|
|
Ao)if is the Doppler width of the gain and absorption
|
|
|
|
lines).
|
|
|
|
In the SML an external heterodyne laser is needed for the FR registration. If the heterodyne laser frequency is
|
|
|
|
highly stabilized with the help of a frequency-feedback system to the reference laser, the main contribution to
|
|
the F/V transformation noise is made by the short-term
|
|
|
|
instability of the laser under investigation.
|
|
|
|
The spectral density of the technical frequency noise of
|
|
|
|
gas lasers in the low frequency range (less than 10 kHz)
|
|
is about - 10"* lO'^ Hz^/Hz. When synchronous detection
|
|
|
|
is used the S/N ratio is determined by the spectral density at the modulation frequency. The problem can't be solved by means of active laser stabilization since the
|
|
AFC system will decrease the frequency fluctuations
|
|
|
|
simultaneously with the signal (A 0)12) and hence the S/N
|
|
|
|
ratio will not be improved. It is possible in Refs. [5, 6]
|
|
|
|
that poor passive short-term stability gave no opportun-
|
|
|
|
ity to obtain any gain in the S/N ratio in case of the FR
|
|
|
|
registration in contrast to AR.
|
|
|
|
DML So,
|
|
|
|
allows one to detect FR with the noise level
|
|
|
|
equal to the natural frequency noises. On the other hand
|
|
|
|
the FR signal, given by Eq. (2), under conditions where
|
|
^1 ~ 1, is determined only by the linear absorption coeffi-
|
|
|
|
cient, i.e., linearly depends on the pressure p_. (As is
|
|
|
|
AR known, for the
|
|
|
|
~ a_
|
|
|
|
p'^ -.)
|
|
|
|
We now estimate the limit of sensitivity of weak line
|
|
|
|
detection by the proposed method. As was mentioned
|
|
|
|
above for the F^*"* methane line, which has an absorption
|
|
|
|
coefficient per unit length of 0.135 m"^ Pa"\ the FR is
|
|
|
|
about 10^ Hz when p_ = 100-200 mPa, £ _ - 0.5 ^o- As-
|
|
|
|
suming that the spectral density of the natural frequency
|
|
|
|
noises is ~ 10"^ Hz-/Hz one may find that the minimum
|
|
|
|
detectable methane pressure is (10"^ - 10 '') mPa. There-
|
|
|
|
FR fore
|
|
|
|
registration with S/N ~ 10''' is possible if
|
|
|
|
~
|
|
|
|
10'^ mPa, T = 1 s and short absorption cells are used.
|
|
|
|
3.3 Resolution of the F^"^^ Methane Line hfs in DML
|
|
For magnetic hfs resolution of the Fi"' line [9] a He-
|
|
Ne/CH4 DML with an internal telescope expander (TE)
|
|
was constructed. The light beam diameter in the absorption cell was about 3 x 10"- m, while the spot size in the active medium was 3 x 10"^ m; t'- = 0.8 m, I'o = 1.8 m. The whole experimental set-up also consisted of the
|
|
|
|
67
|
|
|
|
reference DML and heterodyne laser. The present
|
|
scheme is acceptable when precision spectroscopic inves-
|
|
tigations are made. The reference He-Ne/CH4 DML
|
|
(without TE) has a narrow spectrum (Awg'"' ~ 10 Hz) and
|
|
was constructed according to the scheme described in
|
|
section 3.1. DML/TE was studied in the pressure range jo - ^ 300 mPa. Since there exists a time shift of the
|
|
beat frequency a){2, e.g., due to a slow change of the ac-
|
|
tive medium parameters, synchronous detection of the
|
|
FR with /m = 400 Hz was used. The first and second derivative signals of the FR are
|
|
shown in Figs. 4 and 5 for different p_, /i values. Under high methane pressures (Fig. 4a, p _ = 270 mPa) when
|
|
magnetic hfs isn't resolved the DML/TE frequency sta-
|
|
bilization was made by means of the second derivative of
|
|
the FR. The measurement of the relative frequency sta-
|
|
bility of the DML/TE and DML gave an Allan variance
|
|
a = 0.5 X 10"" (t = 10 s) which is better by two orders
|
|
of magnitude than the one reached in Refs. [5, 6]. (In
|
|
Refs. [5, 6] a SML stabilized by the FR was used.) The asymmetry of the FR and the "crossing" lines [9] are observed clearly at the p _ =40 mPa (Fig. 4b).
|
|
|
|
The spectrograms in Fig. 5a, b were obtained at equal
|
|
|
|
pressure (p_ = 3-4 mPa) but under two different inten-
|
|
|
|
/ sities of the first mode; /i" = 0.2 and
|
|
|
|
^ 1.0. Under
|
|
|
|
conditions corresponding to Fig. 5b, the half width at
|
|
|
|
half maximum (HWHM) of the first derivative FR signal
|
|
|
|
is 7- = (2.7 ± 0.3) kHz. The transit flight time width of
|
|
|
|
the FR is about 5 kHz. The last spectrograms show that
|
|
|
|
the spectral resolution and S/N ratio obtained in the
|
|
|
|
present work are equal to those of Ref. [9] where the hfs of the 7^2"' '^^6 had been resolved for the first time. How-
|
|
|
|
ever the parameters of the experimental set-ups differ in
|
|
|
|
essential ways. Comparison of the absorption particle
|
|
|
|
number in the mode volume and the signal registration
|
|
|
|
time show that the detection sensitivity of the super-
|
|
narrow resonances reached in the DML is about two or-
|
|
|
|
ders higher than the one in Ref. [9].
|
|
|
|
DML In conclusion it may be noted that the
|
|
|
|
with inter-
|
|
|
|
nal absorption cell represents in itself an optical spectro-
|
|
|
|
scope with frequency detection of the signal which may
|
|
|
|
significantly increase the sensitivity and resolution of
|
|
|
|
sub-Doppler spectroscopy and distinguish high quality
|
|
|
|
reference lines as well.
|
|
|
|
a)
|
|
|
|
FR Figure 4. The first and second derivative
|
|
|
|
signals, a) p ^ =
|
|
|
|
270 mPa; the time constant t = 0.3 s; b) p _ = 40 mPa, j = 1 s;
|
|
|
|
the "crossing" lines are observed at the red side of the main
|
|
|
|
components.
|
|
|
|
Figure 5. Magyietic hfs of the F'/' methane line. p_ =
|
|
3-lt mPa, T = 15 s, tight beam diameter = 30 mm, leyigth of
|
|
the cell = 0.8 m; a) /, = 0.2; b)/, = 1.0.
|
|
References
|
|
[1] J. L. Hall, Science 202, 147 (1978). [2] M. A. Gubin et al, Kvant. Elektron. (Moscow) 6, 63 (1979)
|
|
[Sov. J. Quantum Electron. 9, 34 (1979)].
|
|
[3] V. S. Letokhov, Pis'ma Zh. Eksp. Teor. Fiz. 6, 597 (1967) [JETP Lett. 6, 101 (1967)].
|
|
[4] Yu. A. Vdovin et al., Kvant. Elekton. (Moscow) 2, 105 (1973). [Sov. J. Quantum Electron. 2, 565 (1973)].
|
|
[5] G. Kramer et al., Z. Naturforsch. 30a, 1128 (1975). [6] S. N. Bagaev et al., Appl. Pliys. 10, 231 (1976). [7] V. P. Chebotayev, Report at XIX General Assembly of
|
|
URSI, Helsinki, Finland (1978). [8] J. Klapper and J. Frankle, Phase-locked and Frequeyicy-
|
|
Feedback Sijstem.<i, (Academic Press, New York, 1972).
|
|
[9] J. L. Hall and C. J. Borde, Phys. Rev. Lett. .30, 1101 (1973).
|
|
|
|
68
|
|
|
|
X
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
He-Ne (^^^Ig) Lasers at 0.633 fjim (and at 0.604 ixm)
|
|
Fabrizio Bertinetto, Bruno I. Rebaglia, Paolo Cordiale, Sergio Fontana, and Gian Bartolo Picotto
|
|
Istituto di Metrologia G. Colonnetti, Torino, Italy
|
|
Although iodine stabilized, 0.633 |xm lasers are used as practical wavelength standards, no com-
|
|
mon agreement exists as to the operating conditions. It is shown that on the basis of such an agi-eement, reproducibility of ±20 kHz or ±4 x 10"^^v can be attained. This study proposes such conditions and shows that for reproducibility to exceed lO'^^v, certain cavity configurations must be discarded.
|
|
Preliminary observations of strong absorption lines of iodine at the emission wavelength of 0.604 \i.m are also reported.
|
|
Key words: frequency stabilized lasers; frequency standards; wavelength standards.
|
|
|
|
1. He-Ne C^\) Lasers at 0.633 |xm
|
|
1.1 Stability and Reproducibility
|
|
Figure 1 is a plot of the Allan variance of two independently stabilized He-Ne (^^'^12) lasers with the temperature of the iodine cell walls as a parameter. The
|
|
operating conditions were: iodine pressure P = 17.4 Pa
|
|
and modulation depth A v„ -p =6 MHz. The improvement
|
|
in the short term stability due to enhanced signal to noise ratio [1] is evident and can be appreciated in the
|
|
practical utilization of the laser.
|
|
|
|
i=28X
|
|
i=mx
|
|
|
|
r 10-"
|
|
|
|
t=200°C
|
|
|
|
10-'^ c^"
|
|
|
|
1-13 V.
|
|
10
|
|
10^
|
|
|
|
ity was approximately ±5 kHz or 10 "v as shown in
|
|
Fig. 2.
|
|
Similar results can be obtained in any metrological laboratory and it has already been shown that lasers constructed in different laboratories, but under the same
|
|
operating conditions, show a repeatibility of ±20 kHz or ±4 X 10"^^ V [2]. However, for arbitrary operating condi-
|
|
tions and for certain cavity geometries, the repeatibility of the frequency output^ of He-Ne (^^^12) lasers can be no better than ±5 x 10 "^°v, as will be shown below.
|
|
|
|
A3 1 A3 1 CI 1 A2 1 C3 1 Al
|
|
|
|
Bl 10 , C2
|
|
|
|
CI
|
|
1
|
|
B2
|
|
1
|
|
|
|
A2
|
|
1
|
|
B3
|
|
!
|
|
|
|
Bl
|
|
1
|
|
C3
|
|
1
|
|
|
|
Al
|
|
1
|
|
B2
|
|
1
|
|
|
|
B3
|
|
1
|
|
C2
|
|
1
|
|
|
|
N 0 ..
|
|
|
|
X— — ! I
|
|
9 Xo
|
|
|
|
o- -o
|
|
|
|
-X
|
|
N IE
|
|
|
|
I
|
|
|
|
I
|
|
|
|
LD
|
|
|
|
o
|
|
|
|
f\J
|
|
|
|
Figure 1. Allan variance plot for two 0.633 |xm He-Ne (^^^I^)
|
|
lasers at different temperatures of the iodine cell.
|
|
In order to check the frequency reproducibility, three lasers with identical cavity structures and servo-systems were used. Interchanging these servo-systems amongst the lasers, all combinations of lasers and servos were obtained. For each of these combinations separately, frequency differences between the lasers were measured in
|
|
such a way that in every two sets of measurements, i.e.,
|
|
two different combinations of lasers and servos, one laser with its servo-system was kept unaltered so as to be used as a reference laser. It was further assumed that the frequency of this reference laser remained unchanged between two measurements. As a result the reproducibil-
|
|
|
|
-10 i
|
|
|
|
X cavi iy 1
|
|
|
|
ca vity 2 o cavi iy 3
|
|
|
|
Figure 2. Reproducibility of He-Ne C^'/^j lasers constructed at IMGC. The three servo-systems employed are designated A,
|
|
.
|
|
B, and C and the three cavities 1, 2, and 3.
|
|
|
|
•"^This study deals with the frequency measurements of the hfs components d, e, f, g of iodine (^^^12) against a fi.xed reference. Only the behavior of the center of gi-avity of these peaks is reported here. The frequency, therefore, refers to that of the center of gravity. It is worth mentioning here that the gi'oup of hfs components h, i and ./ behaves similarly
|
|
to that of d, e, f and g.
|
|
|
|
69
|
|
|
|
'
|
|
|
|
1.2 Iodine Pressure
|
|
Figure 3 is a typical plot of frequency vs. pressure. Our result differs from that of P. Cerez et al. [3]. The straight line of -9.8 kHz/Pa slope was drawn only through the experimental points for a cold finger tem-
|
|
perature ^ 9 °C. It can be seen that the extrapolation
|
|
below this temperature does not fit the data. At low pressures as the contrast of the peaks becomes poor, the offsets introduced by the electronics of the servo-system become important. Nevertheless the behavior shown in
|
|
Fig. 3 has been obtained consistently.
|
|
|
|
pressure
|
|
Figure 3. Frequency output vs. iodine pressure. Extrapolation
|
|
below t(. = 9 ° C seems incorrect for lasers at 0.633 fim.
|
|
1.3 Misalignment and Cavity Geometry
|
|
The effects of misalignment and cavity geometry are shown in Fig. 4. These curves were obtained by tilting the mirror on the cell side (Ml). Tilting the other mirror (M2) did not change the curves significantly. At maxi-
|
|
mum output power (best alignment), the frequency out-
|
|
put was not affected by the geometry of the laser cavity, except for curve d, in which case there was an offset of approximately 100 kHz. Repeating these measurements with different cavity lengths and laser powers, similar results were obtained which were independent of the output power at best alignment. Shortening the cavity to
|
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150
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b
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N
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-•
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a
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iiao
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curve HI M2^
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<>
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a 1000 1000
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a
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50.
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h 4000 1000
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c flat 500
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0. 0.0
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d 1000 500
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L-340inm
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1
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-H
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H
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— 1— 1
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1
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1
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0.5
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W/Wmax
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—
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i
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h
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1
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1.0
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Figure 4. Effect of misalignment and cavity geometry on fre-
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quency output. Radiis of curvature of Ml and M2 are in milli-
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meters. Mirror reflectivity for curve a 99% for both mirrors, and
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for
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a'
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99.0%
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and
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i% 99.
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.
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The
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effect
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of reflectivity
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and
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hence
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irra-
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diance is synall compared to that of cavity configuration.
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mm 300
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using a shorter tube (otherwise similar to the
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previous ones), the frequency offset observed with the
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same mirrors as of curve d (Fig. 4) was 35 kHz. For this
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cavity length and for mirrors as of curve a and a' output
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was insensitive to misalignment within ±10 kHz.
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Misalignment also had an effect on the slope of the
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modulation dependent frequency shift. For a cavity simi-
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lar to that of curve d (Fig. 4) and at iodine pressure of
|
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17.4 Pa, the slope at Avp.p = 6 MHz was -10.5 kHz/ MHz at best alignment and -4.7 kHz /MHz when the
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power was reduced to 35% by tilting one of the mirrors.
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1.4 Irradiance
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There have been attempts to interpret these results only as an effect of irradiance of the beam traversing the iodine cell [4]. To this end the frequency shift expected from irradiance has been recently measured using two different methods independent of cavity misalignment. The data shown in Fig. 5 were obtained using a laser cavity similar to that of curve a (Fig. 4), but with mirrors of different reflectivities. The error bars are twice the standard deviation. Optical surfaces were cleaned between two measurements using the same mirrors. The dispersion of the frequency output is well within the reproducibiUty of He-Ne { I2) lasers.
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N
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je:
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|
< -2
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50
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|
o 99. 0%-gg. 02
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99. 0Z-99. 43: - 99. 4Z-99. AX
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+-
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-+
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60
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70
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80
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90
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irradiance [W/mm2]
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Figure 5. Frequency output vs. irradimice for a He-Ne f^^^/^j
|
|
laser at 0.633 (jlwl
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|
In another set of measurements the power was varied
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from 44 |jlW to 91 fxW by varying the discharge current
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mA from 2.5
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to 3.5 mA. The variations in the frequency
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|
output were within 1.5 kHz, or 3 x 10"^^v. It can then
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|
be concluded that irradiance had a very small effect on
|
|
the frequency output of a He-Ne (^^^12) laser at
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|
0.633 fxm.
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|
However the proximity of the neighboring lines causes
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some spread in frequency through power broadening.
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Nevertheless, the modulation-dependent shift in the fre-
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|
quency of the center of gravity of a group of adjacent
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|
peaks is not affected by irradiance (see Table 1). That
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the pressure-dependent shift is only slightly affected by
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irradiance can also be seen from Table 1.
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|
1.5 Temperature of the Cell
|
|
Variations in the frequency output of a He-Ne (^^^12) laser with temperature of the iodine cell are shown in
|
|
Fig. 6. At a pressure of 17.4 Pa and Avp-p = 6 MHz
|
|
the frequency shift associated with the cell temperature was found to be approximately 0.16 kHz/K. The effect
|
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|
70
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|
Table 1. Pressure-dependent and modulation-dependent frequency shift at different values of irradiance. The measurements
|
|
were taken in conjunction with those of Fig. 5.
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|
H
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|
Av/P
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|
[ W/mm'] IkHz/Pal [kHz/MHz]
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47
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|
- in p
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54
|
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|
-119
|
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70
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|
-9.8
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|
-10.4
|
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79
|
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|
—
|
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|
-10.7
|
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87
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|
-10.2
|
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|
-10.6
|
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|
and easily saturable. Further investigations are in prog-
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|
ress at IMGC.
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|
|
A laser using a commercial plasma tube is under con-
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|
|
struction and with the proper choice of mirrors is ex-
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|
|
mW pected to give 25
|
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|
|
output at 0.633 p-m. Using two
|
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|
mm mirrors each of 1200
|
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|
|
radius of curvature and 99.8%
|
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|
|
reflectivity, the laser could be operated at 0.604 \x.m [7],
|
|
with a power output of only 25 (jlW. The effect of an
|
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|
|
intracavity cell was the same as that at 0.612 (xm and
|
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|
|
the laser had single mode operation over several hun-
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|
|
dreds of megahertz. Figure 7 shows the emission profile
|
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|
|
and the third derivative signal at an iodine pressure of
|
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|
|
0.8 Pa and a temperature of 160 °C. The lines seen are
|
|
as yet unidentified. A large modulation (nearly 15 mHz
|
|
|
|
peak-to-peak) had to be applied because of a frequency
|
|
jitter of approximately 10 MHz due mainly to the poor
|
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|
|
mechanical mount.
|
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|
|
3001
|
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|
|
25
|
|
'
|
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|
|
—— ————— 10
|
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|
'
|
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1
|
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|
'
|
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15
|
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|
' h-_,
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I
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I
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1
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1
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t-
|
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10
|
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15
|
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20
|
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|
|
lodina prassur* [Pa]
|
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|
|
Figure 6. Frequency output vs. iodine pressure at different
|
|
|
|
temperatures of the cell. For t^, < 200 °C, data below
|
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|
|
=
|
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|
|
9 °C are not shown.
|
|
|
|
shown in Fig. 3 disappears at 200 °C and a solid line has then been drawn for this temperature starting from a
|
|
pressure of 4.1 Pa.
|
|
Heating of the cell seemed to improve the line shape as a small decrease in the modulation-dependent frequency
|
|
shift, from -9.9 kHz/MHz at 28 °C to -8.4 kHz/MHz at 200 °C at a constant iodine pressure of 17.4 Pa, was
|
|
observed.
|
|
|
|
2. He-Ne (^27|^) Laser at 0.604 ixm
|
|
It is known [5, 6] that the 0.612 |xm orange line of HeNe is coincident with iodine transitions which are strong
|
|
|
|
Figure 7. Output power and third harmonic signal vs. laser frequency for a He-Ne ('"^'^I-z) laser at 0.60^ \i.m.
|
|
|
|
3. Conclusions
|
|
|
|
In spite of the fact that the stability of the He-Ne
|
|
C^'^h) lasers at 0.633 |xm approaches 10"^^ v and the reproducibility obtainable in a single laboratory is better
|
|
than ±10 kHz or ±2 x 10"^^ v, the repeatability between
|
|
lasers constructed and operated in different laboratories
|
|
may fall short of 10"^° v in the absence of an agreement
|
|
about the operating conditions and specifications of cavity geometry. Towards using these lasers as practical secondary frequency standards in the optical region, the following operating conditions are suggested:
|
|
|
|
P
|
|
|
|
= (17.4 ± 1) Pa
|
|
|
|
Avp_p = (6 ± 0.2) MHz
|
|
|
|
= (200 ± 5) °C
|
|
|
|
Several cavity configurations give similar performances; however, cavities as of curve d in Fig. 4 should be
|
|
discarded. It is probable that for He-Ne (^^'Is) lasers at 0.612 iJim and at 0.604 [xm a similar problem of choosing the cavity may occur in the future, if the lasers are
|
|
operated with an intracavity cell.
|
|
|
|
References
|
|
ri] p. Cerez and S. J. Bennet, IEEE Trans. Instrum. Meas.
|
|
IM-27, 396 (1978).
|
|
|
|
71
|
|
|
|
[2] J. M. Chartier et a/., IEEE Trans. Instrum. Meas. IM-25, 450.
|
|
[31 P. Cerez et ai, PTB-Bericht Me-17, Ed. by F. Bayer-Helms
|
|
(Physikalisch-Technische Bundesanstalt, Braunschweig, May
|
|
|
|
1977) p. 71.
|
|
|
|
CPEM [4] F. Bertinetto et al.,
|
|
|
|
Digest, Conference on Precision
|
|
|
|
Electromagnetic Measurements, IEEE Cat. No. 78CH1320-
|
|
|
|
1 IM, p. 79.
|
|
[5] P. Cerez et al., IEEE Trans. Instrum. Meas. IM-29, 352
|
|
(1980).
|
|
[6] K. Dschao et al., IEEE Trans. Instrum. Meas. IM-29, 354
|
|
(1980).
|
|
[7] A. D. White and J. D. Rigden, Appl. Phys. Lett. 2, 211
|
|
(1963).
|
|
|
|
72
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Recent Work on 612 nm He-Ne Stabilized Lasers
|
|
|
|
A. Brillet, P. Cerez, and C. N. Man-Pichot
|
|
|
|
Laboratoire de I'Horloge Atomique, Equipe de Recherche du CNRS, associee a TUniversite Paris-Sud, Bat. 221 - Universite Paris-Sud, 91405 - Orsay - France
|
|
|
|
We report on the metrological properties of 612 nm He-Ne lasers frequency stabiHzed on ^^'^12
|
|
|
|
We saturated absorption lines.
|
|
|
|
describe the new results of spectroscopic and metrological interest,
|
|
|
|
obtained both with conventional internal cell devices and with the new technique using an external cell
|
|
|
|
A inside a Fabry-Perot resonator.
|
|
|
|
reproducibility of 6 x 10"^^ is obtained with this last technique.
|
|
|
|
Key words: He-Ne laser; hyperfine predissociation; optical frequency standards; saturated absorption.
|
|
|
|
1. Introduction
|
|
|
|
He-Ne lasers stablized by saturated absorption in ^^'^la
|
|
at 633 nm [1-3] or 612 nm [4] are now widely used in
|
|
|
|
precision interferometry and high resolution spectros-
|
|
|
|
We copy at the 10^^*^ - 10"" precision level.
|
|
|
|
show in this
|
|
|
|
paper how both the high saturation level obtained with
|
|
|
|
internal cell devices and the very high resolution capabil-
|
|
|
|
ity of the external cell technique [5] allowed us to obtain
|
|
new spectroscopic results on the 612 nm R(47)9-2 iodine
|
|
|
|
line, which in turn, helped in improving the metrological
|
|
|
|
properties of these optical frequency standards.
|
|
|
|
2. Experimental Techniques
|
|
|
|
2.1 Internal Cell Devices
|
|
|
|
The cavity of our He-Ne laser is made of three silica
|
|
|
|
rods and contains a commercial He-Ne tube, designed to
|
|
|
|
mW produce 5 to 7
|
|
|
|
of 633 radiation, a 10 cm long iodine
|
|
|
|
cell with Brewster windows, and a Littrow prism for
|
|
|
|
wavelength selection. Its free spectral range is about
|
|
|
|
200 MHz. Because of the low gain at 612 nm, both mir-
|
|
|
|
rors are high reflectivity, and the power emitted through
|
|
|
|
pW each mirror at low iodine pressure is 300
|
|
|
|
at most,
|
|
|
|
strongly depending on the cleanliness of the optical sur-
|
|
|
|
faces. This corresponds to an intracavity power of nearly
|
|
|
|
1 W! Even at the lowest iodine pressure available
|
|
|
|
(0.2 Pa), the laser is single frequency and continuously tunable over 1-200 MHz, due to a differential saturation
|
|
|
|
effect [4].
|
|
|
|
These lasers were used for internal cell saturated absorption studies, with iodine pressures ranging between 2 and 5 Pa. They were also used as sources for the external cell studies, with a much lower iodine pressure (0.1 to 1 Pa). Their emission linewidth, with good passive isolation, has now been reduced to 30 kHz (6 x 10"").
|
|
|
|
2.2 External Cell Technique
|
|
2.2.1 Optical Set-up
|
|
This new saturated absorption technique was first proposed by Cole in 1975 [6], and first demonstrated by C. Pichot-Man et al. [7]. The high sensitivity of this tech-
|
|
nique is easy to understand with simple arguments. Let us consider a resonator with an input mirror Mi, an absorbing cell, and an output mirror M2, having respectively the transmissivities <i, t, and t2 for the field ampli-
|
|
|
|
tude. If the mirrors are perfect, their reflectivities are
|
|
|
|
=
|
|
'"i
|
|
|
|
|1 -
|
|
|
|
and r2 = |1 - i| |^^. At resonance,
|
|
|
|
the intensity transmission of the cavity is then:
|
|
|
|
T= (1 - t r^rif
|
|
|
|
(1)
|
|
|
|
and its variation vdth t is:
|
|
|
|
dt
|
|
|
|
(1 - t rir2)^
|
|
|
|
(2)
|
|
|
|
For
|
|
|
|
ri = 0.98,
|
|
|
|
= 0.98, we get T = 0.45, and
|
|
|
|
dT/dt = 40, which represents the gain in sensitivity
|
|
|
|
compared to the case of a simple saturated absorption ex-
|
|
|
|
periment. Under the same conditions, the energy storage
|
|
|
|
factor inside the resonator is:
|
|
|
|
S=
|
|
|
|
= 22.7
|
|
|
|
(1 - t rir2r
|
|
|
|
(3)
|
|
|
|
Thus this technique allows one to perform saturated absorption spectroscopy even vdth very weak laser sources.
|
|
The numerical values given above correspond approximately to our experimental conditions. Let us note that Eqs. (1) to (3), which do not include the intensity depend-
|
|
ence of t, are valid only for low saturation parameters.
|
|
They constitute, however, a valid approximation, since we always tried to avoid power broadening. If the saturation effects become important, the sensitivity d T/dt further increases, up to the limit of bistabihty.
|
|
A block diagram of the experimental set-up is shown in
|
|
Fig. 1. The resonator is made of two invar rods, 50 cm long. It contains a 20 cm or 35 cm iodine cell, and an anti-reflection coated lens acting as a telescope. The beam waist on mirror M2 can be varied between ivo -0.2 and wq = 3 mm, by translating the lens.
|
|
Feedback to the laser is prevented by a Faraday or an
|
|
acousto-optic isolator.
|
|
|
|
2.2.2 Electronic Set-up
|
|
To operate this spectrometer, one wants to keep the resonator frequency locked onto the laser frequency. This is realized by a conventional servo-loop using frequency modulation of the resonator at 20 kHz (kc in the figure) and synchronous detection. It is important to obtain a very tight lock in order to avoid the excess amplitude noise which would result from a relative frequency jitter between the laser and the resonator.
|
|
|
|
73
|
|
|
|
PZT^
|
|
|
|
Laser/Iodine Lock
|
|
x3
|
|
Cavity/Laser Lock
|
|
|
|
P.S.D.
|
|
|
|
16.5 kc
|
|
|
|
20kc
|
|
|
|
M, L,
|
|
|
|
u
|
|
|
|
Isolator
|
|
|
|
Figure 1. Block diagram of an external cell system.
|
|
|
|
The iodine saturated absorption features are detected by a second frequency modulation, at 5.5 kHz, which is applied simultaneously to the laser and the resonator with the same phase and amplitude so that the signal detected at 5.5 kHz or its 3''^ harmonic is due only to the iodine features and not to a residual frequency mismatch between the laser and the resonator. This signal is synchronously detected and recorded, or used as an error
|
|
signal to lock the laser frequency.
|
|
3. Some Relevant Spectroscopic Properties of 1271^ at 612nm
|
|
3.1 The Saturated Absorption Spectrum
|
|
Figure 2 shows the whole spectrum which can be registered with an internal cell device, completed by higher resolution studies with an external cell. One can easily assign the 21 hyperfine components of R(47)9-2, the 15
|
|
|
|
from R(48)15-5, and the 10 highest frequency components
|
|
|
|
from P(48)ll-3. Furthermore, the spectrum contains over
|
|
|
|
40 additional lines, shown pointing downwards on Fig. 2.
|
|
|
|
They appear clearly only at high intensity, and we could
|
|
|
|
assign most of them to "forbidden,"
|
|
|
|
= 0 transitions
|
|
|
|
and to Doppler generated cross-over resonances between
|
|
|
|
these transitions and allowed ones. Moreover, this as-
|
|
|
|
signment allows one to predict the frequency of some
|
|
|
|
other cross-over resonances which could not be resolved
|
|
|
|
because they were too close to strong allowed transi-
|
|
|
|
tions, like m, q, r (Fig. 3).
|
|
|
|
The relative intensities of the allowed transitions com-
|
|
|
|
pared to R(47)9-2 are about 0.8 for P(48)ll-3 and 0.07 for R(48)15-5 at room temperature. It is possible to enhance by a factor 10 the 15-5 line intensity, using a heated cell.
|
|
|
|
At low power, the computed intensity of the saturated
|
|
|
|
absorption signal is about 10"'* for
|
|
|
|
=0 lines [10] and
|
|
|
|
10"^ for the cross-overs. With increasing power, how-
|
|
|
|
ever, the allowed lines broaden and their intensity satu-
|
|
|
|
AF rates, while the
|
|
|
|
= 0 lines keep increasing linearly,
|
|
|
|
so that the intensity ratio is only about 10 in the usual
|
|
|
|
operating conditions of an internal cell device.
|
|
|
|
3.2 Linewidths and Hyperfine Predissociation
|
|
3.2.1 Instrumental Broadening
|
|
In internal cell devices, the problem has been treated
|
|
earlier [8] for 633 nm lasers. At 612 nm, the linewidth of all the iodine components is about 6 MHz (FWHM),
|
|
mainly due to power broadening. Changing the pressure does not affect the linewidth very much, because any decrease (increase) of the pressure broadening is nearly compensated by an increase (decrease) of the power
|
|
broadening.
|
|
With the external cell technique, it is possible to obtain low saturation parameters. The main source of instrumental broadening is then the pressure broadening which is about 250 kHz /Pa around 1 Pa. Smaller additional ef-
|
|
|
|
oo
|
|
|
|
mXII Ik
|
|
|
|
127,
|
|
|
|
R 47 9-2 + R 48 15-5
|
|
I P48 11-3
|
|
|
|
(stu)
|
|
|
|
+
|
|
|
|
t
|
|
|
|
ed
|
|
IX
|
|
|
|
oo
|
|
|
|
LO
|
|
|
|
g rq p 0
|
|
|
|
(abc)
|
|
|
|
qP oo
|
|
|
|
14 13
|
|
|
|
C,5 C,,
|
|
|
|
Q aQ a
|
|
|
|
m n
|
|
|
|
I
|
|
|
|
k
|
|
|
|
+. + +, +,
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|
(hij) +1
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|
oo
|
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|
12
|
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|
'13
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|
Ci2
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|
10"9
|
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|
11c^C,o
|
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|
Cg
|
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|
'8 8 C7 7
|
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|
cb a
|
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|
oo
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|
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|
e.d
|
|
+
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|
(abc)
|
|
+.
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020:
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|
0
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+
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6 C.
|
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|
|
Figure 2. '-7.2 saturated absorption spectrum at 612 nm. The lines shown pointing
|
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|
|
downwards are forbidden transitions and Doppler generated level crossings. The Af =
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|
|
U 0 lines, and cross-over resonances assignable to R(i7)9-2 are labelled 1 . . .
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|
and Ci
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|
. . . Ci5, respectively.
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|
74
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2
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|
.
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x
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AF=0
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1^ Forbidden Lines
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Level Crossings ^
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|
|
Figure 3. RH7)9-2 hyperfine structure. The intersection of the diagonal lines (which connect some forbidden and allowed resonances) and the frequency axis
|
|
give the cross-over positions.
|
|
|
|
fects come from the laser frequency jitter (30 kHz) and from the finite size of the laser beam waist (10 kHz-mm).
|
|
3.2.2 Radiative Lifetimes and Predissociation
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|
The natural linewidth of a given iodine hyperfine transition can be expressed by the formula
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W = 1 [Fi + Tv + C^JiJ + 1) + Thp],
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|
(4)
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|
|
where Fi is the instrumental broadening, Fv is the radiative Hfetime of the level, Cy J(J + 1) is the gyroscopic predissociation, and Fhp, the hyperfine predissociation rate, is given by [9]:
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X rHp(V,J„F) =
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\o^(I'F,J) 1
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1 3(1 J)^ + 1 J - P2Jt2
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P+
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(2J - 1)(2J + 3)
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(5)
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-av Cv I J
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|
where ay and Cy are the predissociation constants. The
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projection coefficients a{I,F,J) can be determined by fit-
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ting the well-known hyperfine hamiltonian with the
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measured hyperfine splittings [10].
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We specially studied the hyperfine predissociation of
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the R(47)9-2 line by carefully measuring the linewidth of
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all its components, and comparing with Eqs. (4, 5), after a zero pressure extrapolation. For a pressure of 1 Pa, for
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|
instance, the observed line widths vary between 495 kHz for the component p and 1070 kHz for s. Choosing ai 135 10^ S-], Ci = 118 s-\ and Fg + F/ - 2.344 10^ s-\
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the rms difference between experimental and calculated
|
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|
linewidths is only 12 kHz. However, the values of ay and Cy are probably slightly underestimated because of the
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possible presence of a residual background gas in the
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iodine cells: since the collision broadening rates are
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larger for narrow lines than for wider lines due to veloc-
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ity changing collisions [11], the zero pressure extrapola-
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tions would be biased. We estimate our values of ay and
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Cy
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to
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be
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too
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small
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by
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about
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10% ,
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leading
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to
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a9
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= (150 ±
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|
10) X 10^ s^i and C| = (130 ± 10) 8"^ Our results also
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|
|
confirm the negative sign of ay Cy
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|
4. Metrological Results
|
|
4.1 Internal Cell Devices
|
|
In these devices, the most important criterion for choosing the best frequency reference lines is the absence of neighboring lines or cross-over resonances. In this respect, only h, 0, and t are suitable in the R(47)9-2 line. The stability of the lasers locked to 0 or t was com-
|
|
parable with the results obtained at 633 nm with heated
|
|
cells [12]. Their reproducibility has been checked by com-
|
|
parison with a BIPM laser: both lasers produced the
|
|
same frequency within 5 kHz (10"^^). The causes which limit this reproducibility are not understood. They are
|
|
very difficult to isolate experimentally because all the parameters are strongly coupled in these compact systems. Anyway, it seems reasonable to use these simple devices for interferometry at the 10"^" level and to prefer external cell systems for higher precision measurements.
|
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|
|
4.2 External Cell Systems
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|
|
In this case, most lines are well isolated, because they are narrow and because the spectrum is simple, the intensity of forbidden lines being negligible at low power. Since the intensity of a saturated absorption feature is inversely proportional to the square of its vddth (see
|
|
Fig. 4), the figure of merit,
|
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|
|
= jS/N)
|
|
M W'
|
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|
|
(6)
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|
|
is proportional to W"^. It is then strongly recommended
|
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|
|
to use the narrowest lines as frequency references: m, n,
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|
|
p, and t are the best choices, j being perturbed by e
|
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|
|
R(48)15-5.
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|
|
m Using and n components, we obtained a short term
|
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|
|
stability (Allan variance) which varies as 5 x 10
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|
|
We t"^, with a flicker floor at 2 x 10"^^.
|
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|
|
expect in the
|
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|
|
next experiments a tenfold improvement since the excess
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|
|
noise due to the frequency mismatch between the laser
|
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|
|
and the resonator has been greatly reduced.
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|
|
|
The most important step forward is the improvement of the reproducibility which is 300 Hz (6 x 10"^^) \nth these systems. The iodine pressure shift is -4 x 10"^-
|
|
Pa"\ and we can control the iodine pressure with a preci-
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|
|
|
A sion better than 0.05 Pa.
|
|
|
|
variation by a factor of 2 in
|
|
|
|
75
|
|
|
|
Figure 4. First derivative lineshape of R(^7)9-2, h, i, andj components, showing
|
|
hyperfine predissociation.
|
|
|
|
the power from any of the lasers induced no measurable frequency shift. Geometrical effects due to the mismatch of the counterpropagating waves [13] are completely negligible with this technique. The only limitation we could observe was due to the offsets of the servo-loops, so we think we might be able to improve this reproducibility which is already the best one ever reported for a visible optical frequency standard.
|
|
5. Conclusions
|
|
A detailed spectroscopic study of the ^^^l2 properties at
|
|
612 nm allows us to determine the best reference lines to
|
|
be used in internal and external cell devices, and helps in
|
|
understanding the limitations of these systems. The new
|
|
saturated absorption technique using an external cell inside a Fabry-Perot resonator proves to be highly efficient for high resolution spectroscopy and for use in optical frequency standards.
|
|
|
|
References
|
|
[1] G. R. Hanes and C. E. Dahlstrom, Appl. Phys. Lett. 14, 362
|
|
(1969).
|
|
[2] A. J. Wallard, J. Phys. E 5, 926 (1972). [3] A. Brillet, P. Cerez, and H. Clergeot, IEEE J. Quantum
|
|
Electron. QE-10, 526 (1974). [4] P. Cerez and S. J. Bennett, Appl. Opt. 18,1079 (1979). [5] P. Cerez, A. Brillet, C. N. Pichot-Man, and R. Felder,
|
|
IEEE Trans. Instrum. Meas. IM-29, 352 (1980). D [6] J. B. Cole, J. Phys. 8, 1392 (1975).
|
|
[7] C. N. Pichot-Man, P. Cerez, and A. Brillet, in Summaries of
|
|
Contributions to the 11th Annual EGAS Conference (Labo-
|
|
ratoire de Spectroscopie Hertzienne de TENS, Paris,
|
|
1979), p. 133.
|
|
[8] A. Brillet and P. Cerez, Metrologia 13, 137 (1977). [9] M. Broyer, J. Vique, and J. C. Lehmann, J. Chem. Phys. 64,
|
|
4793 (1976). [10] J. P. Picque, private communication.
|
|
[11] J. L. Le Gouet, J. Phys. B 11, 3001 (1978).
|
|
[12] P. Cerez, S. J. Bennet, and C. Audoin, C. R. Acad. Sci. Ser.
|
|
B 286, 53 (1978).
|
|
[13] J. L. Hall and C. J. Borde, Appl. Phys. Lett. 23, 788 (1976).
|
|
|
|
76
|
|
|
|
Precision Measurement and Fundamental Constants II, B. N. Taylor and W. D. Phillips, Eds.,
|
|
Natl. Bur. Stand. (U.S.), Spec. Publ. 617 (1984).
|
|
|
|
Iodine and Methane Stabilized He-Ne Lasers as Wavelength Standards
|
|
Shen Nai-cheng, Wu Yao-xiang, Sun Yi-min, Li Cheng-yang, and Zhang Xue-bin
|
|
National Institute of Metrology, Beijing, P.R.C.
|
|
and
|
|
Wang Chu
|
|
Peking University, Beijing, P.R.C.
|
|
The iodine and methane stabilized lasers designed by NIM and Peking University can be used as wavelength standards. We have compared the frequency differences of the lasers between NIM and BIPM in Paris in April 1980. The relative frequency differences are 2.9 x 10"^^ for iodine and 6.3 x 10~^^ for methane, respectively. When the laser power is given a fixed value, the frequency variation
|
|
of the iodine stabilized laser can be very small. The power shift and standard power value are discussed in this paper.
|
|
Key words: frequency reproducibility; iodine and methane stabilized lasers; power shift; power stand-
|
|
ard value; wavelength standard.
|
|
|
|
1. Introduction
|
|
|
|
Iodine and methane stabilized He-Ne lasers have been
|
|
used as wavelength standards since 1973 [1]. In particu-
|
|
lar, the 633 nm w^avelength of ^^'l2 is very useful and con-
|
|
venient. International intercomparisons of lasers have
|
|
been done many times. We performed the first comparison between NIM and BIPM in April 1980 [2]. The
|
|
results of our comparison were satisfactory. Although
|
|
the construction of our lasers is different from that of BIPM, the frequency difference of the iodine stabilized lasers is less than 3 x 10"^^ This result gives strong
|
|
proof of the good reproducibility among different 633 nm
|
|
iodine stabilized lasers.
|
|
|
|
2. The Results of the Comparison between NIM and BIPM in 1980
|
|
|
|
2.1 The
|
|
|
|
Stabilized He-Ne Laser
|
|
|
|
Table 1 shows the design characteristics of the ^^^2 stabilized lasers. The measurements were done at BIPM, April 2-17, 1980. The frequency difference and standard deviation of the two lasers were each determined from the small matrix of the measured values from the d to g components by a least-squares calculation. The mean fre-
|
|
|
|
quency difference of thirteen measurements was calculated to be
|
|
|
|
/nim2 - /bipm2 = 13.8 kHz, /nimi - /bipm2 = -20.3 kHz,
|
|
|
|
a = 4.5 kHz a = 3.8 kHz
|
|
|
|
In the comparison, all lasers were adjusted to an iodine pressure of 17.3 Pa (15 °C) and a modulation amplitude of 6 MHz. These are standard operation conditions. The
|
|
laser powers are slightly different between NIM and
|
|
BIPM. The power regions used in the measurements were
|
|
|
|
17 |xW < Pnim2 < 27 |jlW,
|
|
|
|
20 (xW < Pnimi < 28 |jlW,
|
|
|
|
pW 25
|
|
|
|
< Pbipm2 < 43 pW.
|
|
|
|
We have also measured the influence of the iodine
|
|
pressure, modulation amplitude, and the laser power on the laser frequency. For example, the pressure shift of
|
|
the/ component is -9.3 and -9.2 kHz/Pa for NIM2 and NIMI, respectively, and the modulation shift of the /
|
|
component is -7.9 kHz/MHzpp for both lasers. For the
|
|
other components, the shifts are slightly different. The
|
|
|
|
Table 1. Design characteristics of I^-stabilized laser.
|
|
|
|
Laser tube
|
|
|
|
l2-ceii Reflective mirror Output power
|
|
|
|
BIPM 2 NIM (1,2)
|
|
|
|
CW301
|
|
25 cm, 3He-2'^Ne
|
|
made in NIM
|
|
11 cm, ^He-™'Ne
|
|
|
|
10 cm 10 cm
|
|
|
|
99.7%
|
|
50 cm
|
|
99.7%
|
|
120 cm
|
|
|
|
99.5%
|
|
oo
|
|
99.7%
|
|
120 cm
|
|
|
|
40 |jlW 25 jiW
|
|
|
|
77
|
|
|
|
power shifts are -0.05, -0.06, and -0.18 kHz/jjiW for NIM2, NIMl, and BIPM2, respectively.
|
|
|
|
2.2 The Methane Stabilized He-Ne Laser
|
|
The mean frequency difference was calculated to be /nimchi - /bich46 = 0.56 kHz, a = 1.29 kHz.
|
|
The coefficient of frequency variation for NIM-CHl on the discharge current in the laser tube is -1.39 kHz/mA. The modulation shift of NIM-CHl is +657 Hz/100 kHzpp.
|
|
For the comparison, the modulation amplitude of
|
|
NIM-CHl was adjusted to 1.2 MHz.
|
|
3. The Results of the Comparison Between NIM2and NIM1 in 1981
|
|
|
|
The frequency difference between l2-stabilized lasers
|
|
NIM2 and NIMl was determined to be 34 kHz at BIPM in 1980. We have measured the difference once again in
|
|
January 1981. The mean value of thirteen measurements
|
|
at various powers was calculated to be
|
|
|
|
/nIM2 ~ / NIMl
|
|
|
|
22.9 kHz ,
|
|
|
|
CT = 9.8 kHz .
|
|
|
|
The laser tubes of NIM2 and NIMl were replaced with new ones which were filled with the isotope ^*^Ne in April
|
|
1981. The other characteristics of the lasers were the same as in 1980. The power of one laser was fixed, but that of the other was changed from its minimum to its maximum during the measurement, then the power condi-
|
|
tion of the two lasers was interchanged. When the region
|
|
of the power variation was within 9 fxW to 42 ixW, the mean frequency difference varied from 7 kHz to 20 kHz and the standard deviations were about 6-11 kHz. So the power shift is too great for good frequency reproducibil-
|
|
ity. But as the powers of the two lasers were adjusted to about 30-32 |jlW, both the mean frequency difference of
|
|
the small matrix and the standard deviations were very
|
|
small. The value of the difference between NIMl and NIM2 was only 6 kHz, with a = 2 kHz. This result is
|
|
better than the intercomparison for NIM at BIPM in 1980. We shall discuss this in the next section.
|
|
|
|
4. The Selection and Measurement of the Standard Value of the Laser Power for Good Reproducibility
|
|
|
|
In order to get good frequency stability and reproducibility, the absorption peak must have a high contrast and
|
|
a narrow width. On the basis of Greenstein's theory [3], when the other operating conditions are fixed, we find
|
|
the contrast of the absorption signal to be roughly proportional to f{X), which is given by:
|
|
|
|
f{X)
|
|
|
|
=
|
|
|
|
(1
|
|
|
|
+ I/Ia)-'^
|
|
|
|
-
|
|
|
|
(1
|
|
|
|
+
|
|
|
|
-1/2
|
|
27//a)
|
|
|
|
(1)
|
|
|
|
X where
|
|
|
|
= IIIa, I is the laser output power, and Ia is
|
|
|
|
the saturation power of the iodine line. The linewidth
|
|
|
|
half width at half maximum is well represented by the
|
|
|
|
relation
|
|
|
|
7 = 7o(l + I/Ia)'''
|
|
|
|
(2)
|
|
|
|
where 70 and 7 are the linewidth without and with power
|
|
W broadening, respectively. If we take I /Ia = 0.6, f{X) = 0.117 = 0.89 /(Z
|
|
(see Fig. 1), the broadening factor (1 -I- I/Ia)^ = 1.26.
|
|
In this case, the contrast and width of the peak is better for a stabilized laser. The reason for selecting a standard
|
|
value of I /IA instead of I is that the contrast and width
|
|
|
|
0.132 0.117 0-12
|
|
|
|
X = l.42,f(X)max = 0-'32
|
|
|
|
0.6 1.42 Figure 1. f(X) versus X.
|
|
|
|
depend on I /Ia- At the same time, the power broadening increases the asymmetry of the line; this is possibly a main source of the power shift. Thus, the power shift
|
|
depends on I /Ia
|
|
We have measured 7 and Ia of NIM2 and NIMl with a
|
|
third harmonic locking technique. The third harmonic
|
|
signal line shape A^ix ) is given [4] by:
|
|
|
|
Asix) = -16x/m^ + i^/mH)
|
|
|
|
X {x(3m2 - Ax"^ + 12)(d + 1 +
|
|
|
|
- x"^)^
|
|
|
|
+ (12a;2 - 3m2 - A)[d - (I + m~ - x^)]!^} (3)
|
|
|
|
where
|
|
|
|
d = [{\ +
|
|
|
|
- x^f + 4x,^2]1172
|
|
|
|
(4)
|
|
|
|
m and X and are the detuning and modulation amplitude
|
|
divided by 7. The shape of the third harmonic signal is shown in Fig. 2.
|
|
We can see from Fig. 2 that the third harmonic signal
|
|
|
|
crosses the axis at three points. Point 0 is the reference
|
|
point of stabilization. The points on the two sides can be
|
|
also locked, but their frequency values and 7 depend on m. Typical relationships between these quantities are il-
|
|
lustrated in Fig. 3. We have measured 7 and Ia by using
|
|
these relationships and the broadening formula of
|
|
Eq. (2). The results are that 70 is 2.1 MHz and 1.9 MHz,
|
|
IA is 54 |jlW and 50 ixW, and / = (0.6) 7^ is 32 fxW and
|
|
30 M-W for NIMl and NIM2, respectively.
|
|
|
|
X Figure 2. Profile diagram of As( x ).
|
|
|
|
78
|
|
|