$^{88}$Sr$^{+}$ optical clock with $7.9\times 10^{-19}$ systematic uncertainty and measurement of its absolute frequency with $9.8\times 10^{-17}$ uncertainty

Abstract: We report on a $^{88}$Sr$^{+}$ single-ion optical clock with an estimated fractional systematic uncertainty of $7.9\times 10^{-19}$. The low uncertainty is enabled by small rf losses, a thorough evaluation of the blackbody-radiation temperature, and our recent measurement of the differential polarizability. A detailed uncertainty evaluation is presented. We also report on two absolute frequency measurements: one against a remote cesium fountain clock and one against International Atomic Time (TAI). The former lasted 12 days and resulted in a frequency value of 444779044095485.49(15) Hz. The latter spanned ten months with monthly optical-clock uptimes between 68% and 99% and yielded a frequency value of 444779044095485.373(44) Hz. With a fractional uncertainty of $9.8\times 10^{-17}$, it is, to our knowledge, the most accurate optical frequency measurement reported to date. Both frequency values are in agreement with other recent measurements, providing further evidence that the 2021 CIPM recommended frequency value is too high by 1.6 times its uncertainty.