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 Recently, the interferometric measurements have been superseded by accurate optical frequency ones.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.