Frequency Ratio of ${}^{199}$Hg and ${}^{87}$Sr Optical Lattice Clocks beyond the SI Limit

Abstract

We report on a frequency ratio measurement of a ${}^{199}$Hg-based optical lattice clock referencing a ${}^{87}$Sr-based clock. Evaluations of lattice light shift, including atomic-motion-dependent shift, enable us to achieve a total systematic uncertainty of $7.2\times 10^{-17}$ for the Hg clock. The frequency ratio is measured to be ${\nu }_{\mathrm{Hg}}/{\nu }_{\mathrm{Sr}}=2.62931420989890960(22)$ with a fractional uncertainty of $8.4\times 10^{-17}$, which is smaller than the uncertainty of the realization of the SI second, i.e., the SI limit.

5 pages, 3 figures

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