Optical frequency measurement of the 1S-3S two-photon transition in hydrogen

This article reports the first optical frequency measurement of the $1\mathrm{S}-3\mathrm{S}$ transition in hydrogen. The excitation of this transition occurs at a wavelength of 205 nm which is obtained with two frequency doubling stages of a titanium sapphire laser at 820 nm. Its frequency is measured with an optical frequency comb. The second-order Doppler effect is evaluated from the observation of the motional Stark effect due to a transverse magnetic field perpendicular to the atomic beam. The measured value of the $1\mathrm{S}_{1/2}(F=1)-3\mathrm{S}_{1/2}(F=1)$ frequency splitting is $2 922 742 936.729 (13) \mathrm{MHz}$ with a relative uncertainty of $4.5\times10^{-12}$. After the measurement of the $1\mathrm{S}-2\mathrm{S}$ frequency, this result is the most precise of the optical frequencies in hydrogen.