We have performed a pure optical frequency measurement of the 2S-8S͞D two-photon transitions in atomic hydrogen and deuterium. These frequencies are directly compared to a new frequency standard, a diode laser stabilized to a two-photon transition at 778 nm in rubidium. We deduce a new value for the Rydberg constant, R` 109 737.315 685 9͑10͒ cm 21 with an uncertainty of 9 3 10 212 . From the isotope shift, we derive a precise value of the 2S Lamb shift in deuterium ͓L 2S-2P 1059.230͑9͒ MHz͔ and the difference of the quadratic charge radii of deuteron and proton. [S0031-9007(96)02260-0] PACS numbers: 31.30.Jv, 06.20.Jr, 21.10.Ft Hydrogen is the simplest atom, and its properties have been calculated very precisely: quantum electrodynamics (QED) calculations have continuously improved to achieve an impressive accuracy, currently of order 10 211 [1]. At the same time, experimental measurements in hydrogen have been performed at a comparable level of precision to deduce the Rydberg constant and to test the QED calculations [2]. Recently, the interferometric measurements have been superseded by accurate optical frequency ones. These measurements need frequency-multiplication chains which link the measured frequency via intermediate standard lasers to the cesium clock. With a frequency chain starting from the methane-stabilized helium-neon laser, Hänsch and co-workers measured the frequency of the 1S-2S two-photon transition with an uncertainty of 1.8 3 10 211 [3]. In our group, we built a frequency chain linking the frequencies of the 2S-8S͞D two-photon transitions to two standard lasers (the iodine-stabilized and the methane-stabilized helium-neon lasers) and reached a precision of 1.3 3 10 211 [4]. Here we present a new optical frequency measurement of the 2S-8S͞D transitions in hydrogen and deuterium with a frequencymultiplication chain. The relative uncertainty is reduced to about 6 3 10 212 and provides a more precise value of the Rydberg constant. In deuterium, we give a precise determination of the 2S Lamb shift and, from the isotope shift, we obtain the difference of the squared proton and deuteron charge radii r 2 d 2 r 2 p . Our frequency chain connects indirectly hydrogen frequencies to the cesium clock (see Fig. 1). The experiment is carried out at two different laboratories, the Laboratoire Primaire du Temps et des Fréquences (LPTF) at the Observatoire de Paris and the Laboratoire Kastler Brossel (LKB) in the Université Pierre et Marie Curie, which are linked by two, 3 km long, optical fibers. The cornerstone of this chain is a new standard, namely a laser diode at 778 nm (i.e., n 385 THz) stabilized to the 5S 1͞2 -5D 5͞2 two-photon transition of rubidium (LD͞Rb laser) [5]. The laser diode is used in an extended cavity configuration, the rubidium cell is placed inside an enhancement cavity, and the transition is detected by monitoring the fluorescence from the radiative cascade 5D-6P-5S. The main metrological features of the LD͞Rb laser are a 4 3 10 213 short term stability for 1s integration time and a...

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The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.

We have performed a pure optical frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, R` 109 737.315 685 16͑84͒ cm 21 (relative uncertainty of 7.7 3 10 212 ) and for the 1S and 2S Lamb shifts L 1S 8172.837͑22͒ MHz and L 2S-2P 1057.8446͑29͒ MHz [respectively, L 1S 8183.966͑22͒ MHz, and L 2S-2P 1059.2337͑29͒ MHz for deuterium]. These are now the most accurate values available. [S0031-9007(99)09458-2] PACS numbers: 06.20.Jr, 21.10.Ft, 31.30.JvFor many years, Doppler free two-photon spectroscopy has been applied to the hydrogen atom in order to test quantum electrodynamics calculations and to improve the precision of the Rydberg constant R` [1]. Recently, the uncertainty of the measurements has been reduced to a level below 10 211 thanks to optical frequencymultiplication chains, which link the measured frequency via intermediate standard lasers to the caesium clock. With such a chain, Hänsch and co-workers have taken advantage of the small natural width of the 1S-2S twophoton transition (1.3 Hz) to measure this frequency with an uncertainty of 3.4 3 10 213 [2]. In our group, we have made absolute frequency measurements of the 2S-8S͞D transitions with an accuracy better than 8 3 10 212 [3]. In this last case, the precision was limited by the line shape analysis which becomes complicated by a large broadening (up to 1 MHz) due to the inhomogeneous light shift. The comparison of the 1S-2S and 2S-8S͞D measurements has provided very precise determinations of R`and of the Lamb shift [2,3]. Nevertheless, in order to confirm our 2S-8S͞D frequency measurements, we have built a new chain to measure the frequencies of another transition, that is the 2S-12D transition. This transition yields complementary information to our study of the 2S-nS͞nD transitions, because it is very sensitive to stray electric fields (the shift due to the quadratic Stark effect varies as n 7 ), and so such a measurement is a stringent test of Stark corrections to the Rydberg levels.In this Letter, we present these new results and make a complete analysis of the optical frequency measurements to determine the best values for R`and the Lamb shifts.Our new frequency chain uses two standard lasers, a laser diode stabilized on the 5S-5D two-photon transition of rubidium (LD͞Rb laser, l 778 nm, n 385 THz) and a CO 2 laser stabilized to an osmium tetraoxyde line (labeled CO 2 ͞OsO 4 , l ഠ 10 mm, n ഠ 29 THz). In 1996, the frequencies of three LD͞Rb lasers, one in the Laboratoire Kastler Brossel (LKB) and two in the Laboratoire Primaire du Temps et des Fréquences (LPTF), were measured with a frequency chain which connected the LD͞Rb laser to the CO 2 ͞OsO 4 standard [4]. More recently, the frequency measurement of this CO 2 ͞OsO 4 standard has been remade with respect to the Cs clock with an uncertainty of 20 Hz (i.e., a relative uncertainty of...

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We present a calculation of the complete set of QED corrections of order mα7 for one-electron two-center systems. Leading corrections of order mα8 are also considered, which allows us to estimate the magnitude of yet uncalculated contributions. The theoretical uncertainty on the frequencies of rovibrational transitions in the hydrogen molecular ions H2+ and HD+, and of two-photon transition in antiprotonic helium is reduced by about 1 order of magnitude, down to (3-4)×10-11 and 10-10, respectively. These results open new perspectives for improved determination of the proton- and antiproton-to-electron mass ratios by precision spectroscopy experiments.

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Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants like the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion in its electronic ground state. We measure the frequency of the v = 0→9 overtone transition of this spectrum with an uncertainty of 2.9 parts-per-trillion through Doppler-free two-photon laser spectroscopy. Leveraging high-precision ab initio calculations we convert our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning-trap determinations of these quantities. This results in an unprecedented precision of 21 parts-per-trillion for the value of the proton-electron mass ratio.