VOLUME 69, NUMBER 16 PHYSICAL REVIEW LETTERS 19 OCTOBER 1992 Precise Frequency Measurement of the 2S-SS/SD Transitions in Atomic Hydrogen: New Determination of the Rydberg Constant F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, and F. Biraben Laboratoire de Spectroscopic Hertzienne de I'Ecole Normale Superieure, Universite Pierre et Marie Curie, Tour 12 E01, 4 place Jussieu, 75252 Paris CEDEX05, France R. Felder Bureau International des Poids et Mesures, Pavilion de Breteuil, 92312 Sevres CEDEX, France O. Acef, J. J. Zondy, P. Laurent, (a) A. Clairon, and M. Abed Laboratoire Primaire des Temps et des Frequences, Bureau National de Metrologie-Observatoire de Paris, 61 avenue de VObservatoire, 75014 Paris, France Y. Millerioux and P. Juncar Institut National de Metrologie-Bureau National de Metrologie, 292 rue St. Martin, 75141 Paris CEDEX 03, France (Received 5 August 1992) We have measured the Rydberg constant by frequency comparison of the three transitions 2S\/i- 851/2, 2S1/2-8D3/2, and ISm-SDsn in hydrogen with the difference of two optical standards, the methane-stabilized He-Ne laser and the iodine-stabilized He-Ne laser. The frequency of the iodine- stabilized He-Ne laser has been remeasured. The new value for the Rydberg constant, R™ = 109737.3156830(31) cm ~ ! , is currently the most precise available. PACS numbers: 06.20Jr, 06.20.Hq, 31.30.Jv The Rydberg constant Roo is important in many areas of physics and chemistry. During the last twenty years, the precise techniques of Doppler-free laser spectroscopy have been applied to atomic hydrogen and the uncertain- ty in R 00 has been reduced drastically [1]. Yet there are several reasons to improve this precision even further. Roo is the natural energy scale of atomic physics. It plays a key role in the least-squares adjustment of the physical fundamental constants [2]. A very precise value of Roo is required to test quantum electrodynamics (QED) calcu- lations on simple systems, for example, to determine the Lamb shift of the hydrogen \S state [3,4]. Finally, the comparison of two Rydberg measurements deduced from different transitions in hydrogen provides a severe test of the Mr dependence of the Coulomb potential [5]. From another point of view, this Mr dependence can be sup- posed exact: As hydrogen has transitions with frequen- cies ranging from the microwave region (transition be- tween circular Rydberg states [6]) to the visible, the hy- drogen atom can be used to check the frequency chains connecting these two frequency domains [7,8]. Until very recently, the most precise Rydberg constant value was given by the 1988 measurement performed by our group in Paris on the 2S\/2-nD$/2 two-photon transi- tions (w =8,10,12) in hydrogen and deuterium [9]. This measurement was based on an interferometric compar- ison between the excitation laser and the iodine-stabilized He-Ne laser (He-Ne/12) at 633 nm. The precision was limited by the uncertainty in the frequency of the He- Ne/h laser (1.6 x 10 ~ 10 ) which had been measured at the National Bureau of Standards (NBS) in 1983 [10]. Our precision relative to the standard was 4.3x 10~ n . The present experiment is based on a new determina- tion of the He-Ne/h standard frequency made at the La- boratoire Primaire des Temps et des Frequences (LPTF) and on a frequency comparison between this standard and the 2S-8S and 2S-&D hydrogen transitions that we have performed at the Laboratoire de Spectroscopie Hertzienne (LSH). In this latest work, the frequency chain between the cesium clock and the frequencies of the 2S-8S/8D transitions is almost continuous and the inter- ferometric method is only used to measure a small fre- quency splitting (88 GHz). Our measurement is the most precise to date with an uncertainty of 2.9 parts in 10 11 . The frequency chain of LPTF connects the He-Ne/h laser at 473 THz to a standard at 29 THz which is a CO2 laser stabilized on an OSO4 line. The frequency of the latter had been measured previously with an uncertainty of 2.7xl0~ 12 [11]. The details of this frequency chain will be published later. The frequency v/ of the / hyperfine component of a He-Ne/h laser of the Institut National de Metrologie (labeled INM12) has been mea- sured: v/=473612353586.0(3.4) kHz. We note that this value is 133 kHz redshifted with respect to the NBS value used in our previous measure- ment. In 1988 we compared our standard laser with the same INM12 laser. For this reason, we can now take into account the new value of the standard frequency to correct and improve our 1988 results. From frequency comparisons with other standard lasers, we can estimate the frequency stability of the INM12 laser, over the 2326 © 1992 The American Physical Society