Laser spectroscopy of the 1S-2Stransition in hydrogen and deuterium: Determination of the 1SLamb shift and the Rydberg constant

We have observed the narrow 1S-2S transition in hydrogen and deuterium with high resolution using Doppler-free two-photon absorption of continuous-wave 243-nm light. The transition frequencies were measured by direct comparison with accurately calibrated lines in the spectrum of the ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}_2^{}{}_{}{}^{}$ molecule. We find the 1S-2S interval to be 2 466 061 414.1(8) MHz in hydrogen and 2 466 732 408.5(7) MHz in deuterium. By combining these results with recent measurements of the Rydberg constant we obtain the values 8172.6(7) and 8183.7(6) MHz for the 1S Lamb shifts in hydrogen and deuterium, respectively. These are the most precise measurements of the 1S Lamb shifts in these atoms and they are in excellent agreement with the theoretical values of 8173.03(9) and 8184.08(12) MHz. Alternatively, if the 1S Lamb shift is supposed known from theory, our measurements determine the Rydberg constant as $R_{\infty }$=109 737.315 73(3) ${\mathrm{cm}}^{\mathrm{-}1}$.