Precision measurement of the 1S ground-state Lamb shift in atomic hydrogen and deuterium by frequency comparison

We have measured the hydrogen and deuterium 1S Lamb shift by direct optical frequency comparison of the 1S-2S and 2S-4S/4D two-photon transitions. Our result of 8172.874(60) MHz for the 1S Lamb shift in hydrogen is in agreement with the theoretical value of 8172.802(40) MHz. For the 1S Lamb shift in deuterium, we obtain a value of 8183.807(78) MHz, from which we derive a deuteron matter radium of 1.945(28) fm. The precision of our value for the 1S Lamb shift has surpassed that of radio frequency measurements of the 2S-2P Lamb shift. By comparison with a recent absolute measurement of the hydrogen 1S-2S transition frequency, we deduce a value for the Rydberg constant ${\mathit{R}}_{\mathrm{\infty }}$=109 737.315 684 9(30) ${\mathrm{cm}}^{\mathrm{-}1}$.