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

Abstract

We report direct measurements of the frequency ratio of the 642 THz ${}^2{S}_{1/2}(F=0)$--${}^2{F}_{7/2}(F=3)$ electric octupole transition in ${}^{171}{\mathrm{Yb}}^{+}$ and the 429 THz ${}^1{S}_0$--${}^3{P}_0$ 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 ${\nu }_{{\mathrm{Yb}}^{+}}/{\nu }_{\mathrm{Sr}}=1.495991618544900537(38)$. This represents one of the most accurate measurements between two different atomic species to date.

9 pages, 4 figures, 1 table

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