Long-distance chronometric leveling with a portable optical clock

Abstract

We have measured the geopotential difference between two locations separated by $457~\mathrm{km}$ by comparison of two optical lattice clocks via an interferometric fiber link, utilizing the gravitational redshift of the clock transition frequency. The $^{87}$Sr clocks have been compared side-by-side before and after one of the clocks was moved to the remote location. The chronometrically measured geopotential difference of $3918.1(2.6)\,\mathrm{m^2 \, s^{-2}}$ agrees with an independent geodetic determination of $3915.88(0.30)\,\mathrm{m^2 \, s^{-2}}$. The uncertainty of the chronometric geopotential difference is equivalent to an uncertainty of $27~\mathrm{cm}$ in height.