Phase-coherent Measurement Of The Hydrogen 1S-2S ... - IEEE Xplore

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997

Phase-Coherent Measurement of the Hydrogen 1S-2S Frequency with an Optical Frequency Interval Divider Chain Thomas Udem, Andreas Huber, Martin Weitz, Dietrich Leibfried, Wolfgang K¨onig, Marco Prevedelli, Alexander Dimitriev, Harald Geiger, and Theodor W. H¨ansch

Abstract— We have measured the absolute frequency of the hydrogen 1S-2S two-photon resonance with an uncertainty of 3.4 parts in 1013 by comparing it with the 28th harmonic of a methane-stabilized 3.39 m He–Ne-laser. A frequency mismatch of 2 THz at the 7th harmonic was bridged with the help of a phase-locked chain of five optical frequency interval dividers. Index Terms—Fundamental constants, hydrogen spectroscopy, metrology, optical frequency comb generator, optical frequency interval divider, optical frequency measurement.

A frequency mismatch of about 2 THz between the dye laser frequency and the 7th harmonic of our infrared He–Ne laser was bridged interferometrically with the help of the measured axial mode spacing of a stable passive reference cavity. At that time we obtained a frequency of (1S-2S) 2 466 061 413 182 (45) kHz, with an uncertainty dominated by drifts of the reference cavity.

II. MEASUREMENTS

I. INTRODUCTION

W

E HAVE demonstrated for the first time a phasecoherent multistage optical frequency interval divider chain, and have used it to measure the absolute frequency of the extremely sharp hydrogen 1S-2S two-photon resonance with an accuracy of 3.4 parts in 10 , surpassing the best previous measurement [1] by more than an order of magnitude. The evaluation of our data gives a frequency (1S-2S) 2 466 061 413 187.34 (84) kHz for the hydrogen 1S-2S energy interval. The uncertainty is limited by the calibration of a transportable methane-stabilized He–Ne laser near 3.39 m which serves as an intermediate frequency reference. Since the simple hydrogen atom permits unique comparisons of experiment and theory, the new measurement will provide a key element for the determination of more accurate values of fundamental quantities, such as the Rydberg constant, the charge radius of the proton, the structure radius of the deuteron, or the electron/proton mass ratio. In an earlier experiment [1] we used a phase-locked harmonic laser frequency chain to measure the frequency of a cw dye laser near 486 nm, the second harmonic frequency of which drives the 1S-2S transition by longitudinal Dopplerfree two-photon excitation of a cold hydrogen beam [2]. Manuscript received June 20, 1996; revised October 1, 1996. This work was supported in part by the Deutsche Forschungsgemeinschaft. T. Udem, A. Huber, M. Weitz, W. K¨onig, H. Geiger, and T. W. H¨ansch are with the Max Planck Institut f¨ur Quantenoptik, 85748 Garching, Germany. D. Leibfried was with the Max Planck Institut f¨ur Quantenoptik, 85748 Garching, Germany. He is now with NIST, Boulder, CO 80303 USA. M. Prevedelli was with the Max Planck Institut f¨ur Quantenoptik, 85748 Garching, Germany. He is now with LENS, Florence, Italy. A. Dimitriev is with the Institute of Laser Physics, Novosibirsk 630090, Russia. Publisher Item Identifier S 0018-9456(97)01808-1.

The present experiment takes advantage of a new concept for visible frequency division, first demonstrated in elementary form some years ago in our laboratory [3]. A laser can be between two forced to oscillate at the precise midpoint and , by servo-controlling so that given frequencies and the the beat frequency between the second harmonic goes to zero. By cascading a number sum frequency stages of such optical frequency interval dividers, an of arbitrary frequency interval can be divided by a factor of , until the beat frequency becomes accessible to microwave counting techniques. Taking advantage of stable and highly reliable grating tuned diode lasers [4] near 848 nm and digital phase-locking techniques with a wide capture range [5], we have constructed a chain of 5 phase-locked interval divider stages which divide THz interval in our hydrogen experiment by a factor the . The residual interval of about 66 GHz is measured via its beat note with the help of a microwave frequency counter. Fig. 1 gives an overview of our experiment. An infrared reference frequency is generated by a transportable methanestabilized He–Ne laser at 3.39 m, which has been constructed at the Institute of Laser Physics, Novosibirsk, Russia, and calibrated in several direct and indirect comparisons with the microwave frequency of the cesium atomic time standard at the PTB in Braunschweig. A NaCl OH color center laser near 1.69 m is electronically phase-locked to the second harmonic , produced in a crystal of AgGaSe , and its output frequency is doubled in a crystal of LiIO , to give a frequency reference near 848 nm. at The first divider stage [6] finds the midpoint between and , i.e., it locks a diode laser to the the dye laser frequency

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UDEM et al.: PHASE-COHERENT MEASUREMENT

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[2] F. Schmidt-Kaler, D. Leibfried, S. Seel, C. Zimmermann, W. K¨onig, M. Weitz, and T. W. H¨ansch, “High-resolution spectroscopy of the 1S-2S transition of atomic hydrogen and deuterium,” Phys. Rev. A, vol. 51, pp. 2789–2800, Apr. 1995. [3] H. R. Telle, D. Meschede, and T. W. H¨ansch, “Realization of a new concept for visible frequency division: Phase locking of harmonic and sum frequencies,” Opt. Lett., vol. 15, pp. 532–534, May 1990. [4] L. Ricci, M. Weidem¨uller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. K¨onig, and T. W. H¨ansch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun., vol. 117, pp. 541–549, June 1995. [5] M. Prevedelli, T. Freegarde, and T. W. H¨ansch, “Phase locking of grating-tuned diode lasers,” Appl. Phys. B, vol. 60, pp. S241–S248, Feb. 1995. [6] R. Wynands, T. Mukai, and T. W. H¨ansch, “Coherent bisection of frequency intervals as large as 530 THz,” Opt. Lett., vol. 17, pp. 1749–1751, Dec. 1992. [7] M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron, vol. 29, pp. 2693–2701, Oct. 1993.

Fig. 1. Scheme of the harmonic laser frequency chain and frequency interval divider chain used in a new phase-coherent precision measurement of the hydrogen 1S-2S resonance frequency.

frequency . The interval of between and is then further reduced by four subsequent divider stages. GHz is measured with a fast The final interval of commercial photodiode, followed by a microwave frequency counter. The entire system can remain locked for periods of hours. Construction details and performance characteristics of the divider chain will be reported elsewhere. In principle, the 2 THz interval could have also been bridged with a much more compact nonlinear frequency comb generator [7]. Experiments to compare this comb generator with our interval divider chain have also been performed in our laboratory. It was found that the two methods for bridging large frequency gaps agree within our current experimental . limitation of The concept of optical interval division becomes even more interesting when combined with optical comb generation. We note that a five-stage interval divider chain, followed by a 3 THz comb generator, can bridge frequency intervals as THz 96 THz. This would be sufficient large as to synthesize and measure any arbitrary optical frequency with our frequency chain, considering the accessible sum and difference frequencies.

Thomas Udem was born on September 25, 1962, in Bayreuth, Germany. From 1987 to 1993, he studied physics at the University of Giessen, Germany, and at the University of Washington, Seattle, WA. In 1993, he received the diploma from the University of Giessen. Since then, he has been pursuing the Ph.D. degree at the Max Planck Institut f¨ur Quantenoptik, Garching, Germany. His principal fields are laser physics, nonlinear optics, and optical frequency measurements.

Andreas Huber was born in Kaufbeuren, Germany, on March 3, 1968. He received the Diploma in physics in 1993 from the Ludwig-Maximilians University, Munich, Germany. He is now pursuing the Ph.D. degree Since 1992, he has been working at the Max Planck Institut f¨ur Quantenoptik, Garching, Germany, on high-resolution spectroscopy of atomic hydrogen with the aim of testing QED and measuring fundamental atomic constants.

ACKNOWLEDGMENT The authors are indebted to G. Kramer and B. Lipphardt, PTB, Braunschweig, and D. A. Tyurikov, P.N. Lebedev Institute, Moscow, for their essential support in the calibration of the infrared reference laser. They also thank M. Ohtsu and M. Kourogi, who made a frequency comb generator available to them. REFERENCES [1] T. Andreae et al., “Absolute frequency measurement of the hydrogen 1S-2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett., vol. 69, pp. 1923–1926, Sept. 1992.

Martin Weitz was born in Mannheim, Germany, on October 26, 1964. He received the Diploma in physics from the Technische Universit¨at M¨unchen in 1989, and the Ph.D. degree from the Universit¨at M¨unchen in 1992. His thesis topic was Lamb shift measurements on atomic hydrogen. He was with Stanford University, Stanford, CA, involved in research on atom interferometers, and he is now a Research Physicist, Max Planck Institut f¨ur Quantenoptik, Garching, Germany. His current research interests include atom interferometry, hydrogen spectroscopy, and laser cooling.

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Dietrich Leibfried was born in Stuttgart, Germany, in 1965. He received the diploma in physics from the Ludwig-Maximilians University, Munich, Germany, in 1991. From 1992 to 1995, he pursued the Ph.D. degree in physics at the Max-Planck Institute for Quantum Optics, Garching, Germany, researching high-precision laser spectroscopy in atomic hydrogen. Since 1995, he has been a Guest Researcher in the Ion Storage Group, NIST, Boulder, investigating precise clocks, quantum control, and quantum logic in trapped ions. Dr. Leibfried shared the 1993 Helmholtz Award of the PTB for high precision measurements.

Alexander Dimitriev, photograph and biography not available at the time of publication.

Harald Geiger, photograph and biography not available at the time of publication.

Theodor W. H¨ansch, photograph and biography not available at the time of publication. Wolfgang K¨onig, photograph and biography not available at the time of publication.

Marco Prevedelli, photograph and biography not available at the time of publication.