Optical frequency ratio of a ${}^{171}\mathrm{Yb}^+$ single-ion clock and a ${}^{87}\mathrm{Sr}$ lattice clock

We report direct measurements of the frequency ratio of the 642 THz ${}^2S_{1/2} (F=0)$--${}^2F_{7/2} (F=3)$ electric octupole transition in ${}^{171}\mathrm{Yb}^+$ and the 429 THz ${}^1S_0$--${}^3P_0$ transition in ${}^{87}\mathrm{Sr}$. A series of 107 measurements has been performed at the Physikalisch-Technische Bundesanstalt between December 2012 and October 2019. Long-term variations of the ratio are larger than expected from the individual measurement uncertainties of few $10^{-17}$. The cause of these variations remains unknown. Even taking these into account, we find a fractional uncertainty of the frequency ratio of $2.5 \times 10^{-17}$, which improves upon previous knowledge by one order of magnitude. The average frequency ratio is $\nu_{\mathrm{Yb}^+} / \nu_{\mathrm{Sr}} = 1.495\,991\,618\,544\,900\,537(38)$. This represents one of the most accurate measurements between two different atomic species to date.