Phase-Coherent Measurement of the Hydrogen1S−2STransition Frequency with an Optical Frequency Interval Divider Chain

We have measured the absolute frequency of the hydrogen $1S-2S$ two-photon resonance with an accuracy of 3.4 parts in ${10}^{13}$ by comparing it with the $28\mathrm{th}$ harmonic of a methane-stabilized $3.39\mu \mathrm{m}$ He-Ne laser. A frequency mismatch of 2.1 THz at the $7\mathrm{th}$ harmonic is bridged with a phase-locked chain of five optical frequency interval dividers. From the measured frequency $f_{1S-2S}=2\mathrm{}466061413187.34\left(84\right)\mathrm{kHz}$ and published data of other authors we derive precise new values of the Rydberg constant, $R_{\infty }=10\mathrm{}973731.568639\left(91\right){\mathrm{m}}^{-1\mathrm{}}$ and of the Lamb shift of the $1S$ ground state, $L_{1S}=8172.876\mathrm{}\left(29\right)\mathrm{MHz}$. These are now the most accurate values available.