Optical clocks with accuracy validated at the 19th digit

Abstract

We report a comprehensive evaluation of all known sources of systematic uncertainty for two independent ${}^{176}$Lu${}^{+}$ single-ion optical references, finding total systematic uncertainty of $1.1\times 10^{-19}$ and $1.4\times 10^{-19}$ for the two individual systems and $9.6\times 10^{-20}$ for the difference. Through direct comparison via correlation spectroscopy, we demonstrate a relative frequency agreement of $-2.4\pm (5.7{)}_{\mathrm{stat}}\pm (1.0{)}_{\mathrm{sys}}\times 10^{-19}$, where `stat' and `sys' indicate the statistical and systematic uncertainty, respectively. The comparison uncertainty is statistically limited after approximately 200 hours of averaging with a measurement instability of $4.8\times 10^{-16}(\ddot{I}„/\mathrm{s}{)}^{-1/2}$.

25 pages, 10 figures, 2 tables