High-Stability Single-Ion Clock with $5.5\times {10}^{-19}$ Systematic Uncertainty

We report a single-ion optical atomic clock with fractional frequency uncertainty of $5.5\times {10}^{-19}$ and fractional frequency stability of $3.5\times {10}^{-16}\mathrm{/}\sqrt{\tau \mathrm{/}\mathrm{s}}$, based on quantum logic spectroscopy of a single ${}^{27}$Al${}^{+}$ ion. A co-trapped ${}^{25}$Mg${}^{+}$ ion provides sympathetic cooling and quantum logic readout of the ${}^{27}$Al${}^{+}$ ${}^1$S${}_0{\leftrightarrow }^3$P${}_0$ clock transition. A Rabi probe duration of 1 s, enabled by laser stability transfer from a remote cryogenic silicon cavity across a 3.6 km fiber link, results in a threefold reduction in instability compared to previous ${}^{27}$Al${}^{+}$ clocks. Systematic uncertainties are lower due to an improved ion trap electrical design, which reduces excess micromotion, and a new vacuum system, which reduces collisional shifts. We also perform a direction-sensitive measurement of the ac magnetic field due to the RF ion trap, eliminating systematic uncertainty due to field orientation.