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

TL;DR

This paper reports a highly precise measurement of the frequency ratio between a ${}^{171} ext{Yb}^+$ single-ion clock and a ${}^{87} ext{Sr}$ lattice clock, achieving an order of magnitude improvement in accuracy over previous results.

Contribution

The study provides the most accurate measurement to date of the frequency ratio between these two atomic clocks, with detailed analysis of long-term variations and uncertainties.

Findings

Fractional uncertainty of $2.5 imes 10^{-17}$

Average frequency ratio $ u_{ ext{Yb}^+} / u_{ ext{Sr}} = 1.495991618544900537(38)

Long-term variations exceed expectations from measurement uncertainties.

Abstract

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.