Phase-Coherent Measurement of the Hydrogen<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi mathvariant="italic">S</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant="italic">S</mml:mi></mml:math>Transition Frequency with an Optical Frequency Interval Divider Chain

We have measured the absolute frequency of the hydrogen $1S\ensuremath{-}2S$ 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 $3.39\ensuremath{\mu}\mathrm{m}$ 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 ${f}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2466061413187.34(84)\mathrm{kHz}$ and published data of other authors we derive precise new values of the Rydberg constant, ${R}_{\ensuremath{\infty}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10973731.568639(91){\mathrm{m}}^{\ensuremath{-}1}$ and of the Lamb shift of the $1S$ ground state, ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8172.876(29)\mathrm{MHz}$. These are now the most accurate values available.