An Al${}^{+}$ clock with $1.6\times {10}^{-18}$ systematic uncertainty and its frequency ratios

Advances in optical clocks motivate a redefinition of the second, requiring rigorous evaluations of systematic uncertainties and robust consistency among the clocks. Here, we report the full evaluation of the systematic frequency shifts of an ${}^{27}{\mathrm{A}\mathrm{l}}^{+}$ single-ion clock, and the measurement of its absolute frequency and frequency ratio with a ${}^{87}$Sr optical lattice clock at PTB. The evaluated total systematic fractional frequency uncertainty is $1.6\times {10}^{-18}$, mainly limited by the accuracy of the relevant atomic coefficients and by background gas collisions. The absolute frequency of the clock has been measured to be ${\nu }_{{\mathrm{A}\mathrm{l}}^{+}}=1121015393207859.19(24)$Hz, obtained by comparison with two primary caesium fountain clocks at PTB. The frequency ratio between the Al and Sr optical clocks has been determined to be ${\nu }_{{\mathrm{A}\mathrm{l}}^{+}}\mathrm{/}{\nu }_{{}^{87}\mathrm{S}\mathrm{r}}=2.611701431781462668(36)$, limited by the accuracy of the Sr clock. This ratio differs by $8.6\sigma$ and $1.2\sigma$ from the 2021 and 2025 frequency ratio published by the BACON collaboration, respectively. These results represent an important contribution toward a future redefinition of the second using optical clocks, and underscore the importance of independent measurements of clock-candidate frequency ratios across different institutions.