Frequency Comparison of $^{171}{\text {Yb}}^+$ Ion Optical Clocks at PTB and NPL via GPS PPP

We used precise point positioning, a well-established GPS carrier-phase frequency transfer method to perform a direct remote comparison of two optical frequency standards based on single laser-cooled $^{171} {\text {Yb}}^+$ ions operated at the National Physical Laboratory (NPL), U.K. and the Physikalisch-Technische Bundesanstalt (PTB), Germany. At both institutes, an active hydrogen maser serves as a flywheel oscillator which is connected to a GPS receiver as an external frequency reference and compared simultaneously to a realization of the unperturbed frequency of the ${^2S_{1/2}(F=0)-{^2D_{3/2}}(F=2)}$ electric quadrupole transition in $^{171} {\text {Yb}}^+$ via an optical femtosecond frequency comb. To profit from long coherent GPS-link measurements, we extrapolate the fractional frequency difference over the various data gaps in the optical clock to maser comparisons which introduces maser noise to the frequency comparison but improves the uncertainty from the GPS-link instability. We determined the total statistical uncertainty consisting of the GPS-link uncertainty and the extrapolation uncertainties for several extrapolation schemes. Using the extrapolation scheme with the smallest combined uncertainty, we find a fractional frequency difference $y({\text {PTB}})-y({\text {NPL}})$ of $-1.3\times 10^{-15}$ with a combined uncertainty of $1.2\times 10^{-15}$ for a total measurement time of 67 h. This result is consistent with an agreement of the frequencies realized by both optical clocks and with recent absolute frequency measurements against caesium fountain clocks within the corresponding uncertainties.