Precision Measurement of the Hydrogen1S−2SFrequency via a 920-km Fiber Link

We have measured the frequency of the extremely narrow $1S\mathrm{\text{−}}2S$ two-photon transition in atomic hydrogen using a remote cesium fountain clock with the help of a 920 km stabilized optical fiber. With an improved detection method we obtain $f_{1S\mathrm{\text{−}}2S}=2466061413187018(11)\mathrm{Hz}$ with a relative uncertainty of $4.5\times {10}^{-15}$, confirming our previous measurement obtained with a local cesium clock [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)]. Combining these results with older measurements, we constrain the linear combinations of Lorentz boost symmetry violation parameters $c_{(TX)}=(3.1\pm 1.9)\times {10}^{-11}$ and $0.92c_{(TY)}+0.40c_{(TZ)}=(2.6\pm 5.3)\times {10}^{-11}$ in the standard model extension framework [D. Colladay, V. A. Kostelecký, Phys. Rev. D. 58, 116002 (1998)].