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International audience; We propose experiments with atomic hydrogen gas at ultra-low temperatures T

The aim of our experiment is to improve the spectroscopy of atomic hydrogen in order to determine the Rydberg constant and contribute to the proton radius puzzle. Our experimental setup allows us to reach a statistical uncertainty of 2.1 kHz on the measurement of the 1S-3S transition frequency. Our latest study of the systematic effects yields a new value of this transition frequency that is five times more precise than our previous determination, contributing to shedding light on the proton radius puzzle.

We present a new measurement of the $1S\ensuremath{-}3S$ two-photon transition frequency of hydrogen, realized with a continuous-wave excitation laser at 205 nm on a room-temperature atomic beam, with a relative uncertainty of $9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$. The proton charge radius deduced from this measurement, ${r}_{p}=0.877(13)\text{ }\text{ }\mathrm{fm}$, is in very good agreement with the current CODATA-recommended value. This result contributes to the ongoing search to solve the proton charge radius puzzle, which arose from a discrepancy between the CODATA value and a more precise determination of ${r}_{p}$ from muonic hydrogen spectroscopy.

International audience; This paper gives a review of the experiments performed since the 1980s at the Laboratoire Kastler Brossel in Paris on two-photon spectroscopy of atomic hydrogen. Firstly devoted to the 2S–nS and 2S–nD transitions, they are currently running on the 1S–3S transition at 205 nm. During all that time, they were inspired by the plentiful ideas proposed by Ted Hänsch and were complementary with the measurements developed in parallel in his groups.This article is part of the topical collection “Enlightening the World with the Laser” - Honoring T. W. Hänsch guest edited by Tilman Esslinger, Nathalie Picqué, and Thomas Udem.

We calculate the cross-damping frequency shift of a laser-induced two-photon transition monitored through decay fluorescence, by adapting the analogy with Raman scattering developed by Amaro et al. [P. Amaro et al., PRA 92, 022514 (2015)]. We apply this method to estimate the frequency shift of the 1S-3S transition in hydrogen and deuterium. Taking into account our experimental conditions, we find a frequency shift of less than 1 kHz, that is smaller than our current statistical uncertainty., Comment: 7 pages, 5 figures

The aim of our experiment is to improve the spectroscopy of atomic hydrogen in order to determine the charge radius of the proton. A new continuous laser source at 205 nm allows us to reach a statistical uncertainty of 2.2 kHz on the measurement of the 1S-3S transition frequency. This uncertainty could be sufficient to clarify the proton radius puzzle, however there remain systematic effects that are currently under study.

The GBAR project (Gravitational Behaviour of Anti hydrogen at Rest) at CERN, aims to measure the free fall acceleration of ultracold neutral anti hydrogen atoms in the terrestrial gravitational field. The experiment consists preparing anti hydrogen ions (one antiproton and two positrons) and sympathetically cooling them with Be (+) ions to less than 10 mu K. The ultracold ions will then be photo-ionized just above threshold, and the free fall time over a known distance measured. We will describe the project, the accuracy that can be reached by standard techniques, and discuss a possible improvement to reduce the vertical velocity spread.

For very high-precision spectroscopy such as the two photon 1S–nS transitions in hydrogen, the ability to measure precisely the absolute frequency of the excitation laser is required together with the best possible signal-to-noise ratio for the fluorescence signal. In the context of our experiment on the 1S–3S transition, we present the specificities of our optical frequency comb apparatus, as well as a new detection scheme that makes use of the spatial information provided by a CCD camera detector.PACS No.: 39.30.+w

The contribution of the root mean square (RMS) proton charge radius to the Lamb shift (2S–2P energy difference) in muonic hydrogen (μp) amounts to 2%. Apart from the uncertainty on this charge radius, theory predicts the Lamb shift with a precision on the ppm level. We are going to measure ΔE (2 S1/2(F=1)–2 P3/2(F=2)) in a laser resonance experiment to a precision of 30 ppm (i.e., 10% of the natural linewidth) and to deduce the RMS proton charge radius with 10−3 relative accuracy, 20 times more precise than presently known. The most important requirement for the feasibility of such an experiment, namely the availability of a sufficient amount of long lived metastable μp atoms in the 2S state, has been investigated in a recent experiment at PSI. Our analysis shows that in the order of one percent of all muons stopped in low pressure hydrogen gas form a long lived μp(2S) with a lifetime of the order of 1 μs. The technical realization of our experiment involves a new high intensity low energy muon beam, an efficient low energy muon entrance detector, a randomly triggered 3 stage laser system providing the 0.5 mJ, 7 ns laser pulses at 6.02 μm wavelength, and a combination of a xenon gas proportional scintillation chamber (GPSC) and a microstrip gas chamber (MSGC) with a CsI coated surface to detect the 2 keV X rays from theμp(2P → 1S) transition.

We have performed a pure optical frequency measurement of the $2S\ensuremath{-}12D$ 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, ${R}_{\ensuremath{\infty}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}109737.31568516(84){\mathrm{cm}}^{\ensuremath{-}1}$ (relative uncertainty of $7.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$) and for the $1S$ and $2S$ Lamb shifts ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8172.837(22)\mathrm{MHz}$ and ${L}_{2S\ensuremath{-}2P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1057.8446(29)\mathrm{MHz}$ [respectively, ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8183.966(22)\mathrm{MHz}$, and ${L}_{2S\ensuremath{-}2P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1059.2337(29)\mathrm{MHz}$ for deuterium]. These are now the most accurate values available.

We have measured the frequencies of three diode lasers stabilized on the 5 S 1 2 (F = 3)−5 D 5 2 (F = 5) two-photon transition in rubidium at λ = 778.1 nm, with an uncertainty of 1 kHz, using BNM-LPTF frequency synthesis chain starting from a CO 2 OsO 4 reference laser at 10.3 μm. We show that this frequency chain is able to reach the 10−13 resolution level. After a discussion of the systematic effects that may shift the resonance, the transition frequency is found to be ν = 385 285 142 378.280 ± 2 kHz.

An absolute optical frequency measurement is made of the hyperfine components of the 5S 1 2 -5D 3 2 two-photon transitions in rubidium with an uncertainty of 1.3×10-11. This is carried out in a simple way by taking advantage of the near coincidence between the two-photon frequency at λ=778 nm in Rb and the frequency difference of two HeNe lasers, stabilized respectively to an iodine line at λ=633 nm and a methane transition at λ=3.39 μm used as reference. This measurement provides a new optical frequency reference in the visible range.

A very precise measurement of the Rydberg constant is performed using a direct-frequency comparison of the 2S-8S and 2S-8D two-photon transitions in atomic hydrogen with the difference of two optical standards connected to a frequency chain. >

We have measured the Rydberg constant by frequency comparison of the three transitions 2S 1/2 -8S 1/2 , 2S 1/2 -8D 3/2 , and 2S 1/2 -8D 5/2 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 ∞=109 737.315 6830(31) cm -1 , is currently the most precise available

We report the latest advances in the Doppler-free spectroscopy of the 1S–3S transition in hydrogen. A new continuous ultra-violet source has been developed and delivers a power level of 15 mW. With this setup, the statistical uncertainty on the 1S–3S transition frequency measurement is 2.2 kHz. Combined with the 1S–2S frequency, absolute accuracy at that level would significantly enlighten the proton radius puzzle.

The determination of the proton rms charge radius with an accuracy of 10−3 is the main goal of our experiment, opening the way to check bound‐state QED predictions in hydrogen to a level of 10−7. The principle is to measure the 2S1/2(F = 1) − 2P3/2(F = 2) energy difference in muonic hydrogen (μ−p) by infrared laser spectroscopy to a precision of 30 ppm. Very low‐energy negative muons are stopped in 0.6 mbar of hydrogen gas, where, following the μ− atomic capture and cascade, 1% of the muonic hydrogen atoms form the metastable 2S state with a lifetime of 1.3 μs. A 6 μm laser pulse is used to drive the 2S → 2P transition. When on resonance, the laser induces the transition, and the subsequent muonic deexcitation to the 1S state emits a 1.9 keV x ray which is detected by avalanche photodiodes. The resonance frequency, and hence the Lamb shift and the proton charge radius, is determined by measuring the rate of laser‐induced x rays as a function of the laser wavelength. Some details of the experiment, recent measurements and improvements will be presented.

We describe the modified LPTF frequency synthesis chain, which starts from the cesium referenced CO/sub 2//OsO/sub 4/ laboratory standard. This chain, with variations, is able to cover the whole visible spectrum. A particular scheme is given in order to measure the 385.3-THz frequency of the two-photon transitions in rubidium. To secure the phase lock, the diode lasers' linewidths have to be reduced. We report a 10-Hz beatnote linewidth obtained with two diode lasers stabilized on the same high-finesse cavity. >

We have stabilized two laser diodes on the hyperfine components of the 5D/sub 3/2/ and 5D/sub 5/2/ two-photon transitions in natural rubidium (v=385 THz). We have carefully investigated the metrological features of these devices. So far we obtain a frequency stability in terms of the Allan variance of 3.10/sup -13/./spl tau//sup - 1/2 / up to 2000 s and a frequency repeatability of the order of 10/sup -12/. The frequency difference between the two devices is 1.7 kHz under identical operating conditions. >

The high resolution two-photon spectroscopy of hydrogen is often limited by the second-order Doppler effect. To determine this effect, we apply a magnetic field perpendicular to the atomic beam. This field induces a quadratic motional Stark shift proportional, as the second-order Doppler effect, to v(2) (v atomic velocity). For some magnetic field, these two effects are opposite and the total shift due to the atomic velocity is reduced. We present the first observation of this effect for the 1S-3S transition in hydrogen.

We present the optical frequency measurements of the 2S-8S/D and 2S-12D two-photon transitions in hydrogen and deuterium. From an analysis taking into account these results and the very accurate measurements of the 1S-2S transition, we show that the optical frequency measurements have superseded the microwave determination of the 2S Lamb shift and we deduce optimized values for the Rydberg constant and for the 1S and 2S Lamb shifts. We report also the recent development of our 1S-3S experiment.

A measurement of the 2S Lamb shift (2S−2P energy difference) in muonic hydrogen (μ−p) is being prepared at the Paul Scherrer Institute (PSI). The goal of the experiment is to measure the Lamb shift with 30 ppm precision and to deduce the root mean square (rms) proton charge radius with 10−3 relative accuracy, 20 times more precise than presently known. The experiment is based on the availability of long-lived metastable muonic hydrogen atoms in the 2S state which has been investigated in a recent series of experiments at PSI. From the low-energy part of the initial kinetic energy distribution of μp(2S) atoms we determined the fraction of long-lived μp(2S) to be ∼1.5% for H2 gas pressures between 1 and 64 hPa. Another analysis involving μp(1S) with a kinetic energy of 0.9 keV originating from quenching of thermalized μp(2S) via the resonant process μp(2S)+H2→{[(ppμ)+]*pee}*→μp(1S)+p+…+2 keV gives the same result. This is the first direct observation of long-lived μp(2S) atoms. The realization of the μp Lam...

We have performed the first pure frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. These frequencies are compared to two optical standards, the CO/sub 2/ laser stabilized on the OsO/sub 4/ molecule and the optical rubidium laser standard (LD/Rb) (namely, a laser diode at 778 nm stabilized on the 5S/sub 1/2/-5D/sub 5/2/ two-photon transition of rubidium). The main part of the experiment is located in the Laboratoire Kastler-Brossel (LKB), one part of the frequency chain is in the Laboratoire Primaire du Temps et des Frequences (LPTF), and two 3 km long optical fibers link the two parts of this experiment. The new value of the Rydberg constant is R/sub /spl infin//=109 737.315 686 06 (79) cm/sup -1/.

A frequency chain, derived from the one used to measure the absolute frequency ((nu) $= 473 THz) of the He-Ne/I 2 optical standard, is currently being implemented in order to measure the frequency of a diode laser stabilized on the two-photon transition of rubidium vapor. The measurement scheme is based on the comparison of the frequency of this near-IR potential secondary standard to the 13th harmonic frequency of the R(12)-CO 2 /OsO 4 LPTF secondary standard at (nu) equals 29.096 THz. Recent results on the frequency synthesis are reported, enabling the testing of long-term stability of this Rb-locked system with respect to the IR reference standard.

We have studied the hyperfine structure of the 5S1/2‐5D3/2,5/2 two‐photon transition in rubidium. Stabilizing a titanium‐sapphire laser on some of these transitions we have carefully investigated their metrological potential. The development of a new frequency standard at λ=778 nm may be expected soon. This will have performance similar to that of the (He‐Ne)/CH4 laser at λ=3.39 μm. With these two references at one’s disposal it will be possible to measure, in a simple way, the absolute frequency of the (He‐Ne)/I2 laser at λ=633 nm with an accuracy of some parts in 1012: this is of great interest for length metrology.

We have performed a new measurement of the Rydberg constant by frequency comparison of the 2S–8S and 2S–8D two‐photon transitions in hydrogen with the difference of two optical standards connected to a frequency chain. Our result is: R∞=109 737.315 6830 (31) cm−1.