Towards the optical second: verifying optical clocks at the SI limit

The pursuit of ever more precise measures of time and frequency motivates redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on the microwave hyperfine transition in ¹³³Cs, it is necessary to measure the absolute frequency of candidate optical standards relative to primary cesium references. Armed with independent measurements, a stringent test of optical clocks can be made by comparing ratios of absolute frequency measurements against optical frequency ratios measured via direct optical comparison. Here we measure the ${}^1\text{S}_0\to {}^3\text{P}_0$ transition of ¹⁷¹Yb using satellite time and frequency transfer to compare the clock frequency to an international collection of national primary and secondary frequency standards. Our measurements consist of 79 runs spanning eight months, yielding the absolute frequency to be 518 295 836 590 863.71(11) Hz and corresponding to a fractional uncertainty of 2.1 × 10^-16. This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty <3 × 10^-16, limited for the first time by the current realization of the second in the International System of Units (SI). Doing so represents a key step towards an optical definition of the SI second, as well as future optical time scales and applications. Furthermore, these high accuracy measurements distributed over eight months are analyzed to tighten the constraints on variation of the electron-to-proton mass ratio, $\text{micro}=m_e/m_p$ . Taken together with past Yb and Sr absolute frequency measurements, we infer new bounds on the coupling coefficient to gravitational potential of $k_{\text{micro}}=(-1.9\pm 9.4)\times {10}^{-7}$ and a drift with respect to time of $\frac{\dot{\text{micro}}}{\text{micro}}=(5.3\pm 6.5)\times {10}^{-17}/\text{yr}$ .