An ¹¹⁵In⁺-¹⁷²Yb⁺ Coulomb crystal clock with 2.5×10⁻¹⁸ systematic uncertainty

We present a scalable mixed-species Coulomb crystal clock based on the ¹S₀ ↔ ³P₀ transition in ¹¹⁵In⁺. ¹⁷²Yb⁺ ions are co-trapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In⁺-3Yb⁺ crystal, achieving a relative systematic uncertainty of 2.5×10⁻¹⁸ and a relative frequency instability of 1.6×10⁻¹⁵/√τ/1\;s. We report on an absolute frequency measurement with an uncertainty of 1.3×10⁻¹⁶ and optical frequency ratios relative to the ¹⁷¹Yb⁺ (E3) and ⁸⁷Sr clock transitions with fractional uncertainties of $4.4$ and $4.7$ parts in 10¹⁸, respectively. The latter are among the most precise measurements of frequency ratios to date and improve upon the previous uncertainty of the ¹¹⁵In⁺/⁸⁷Sr ratio by two orders of magnitude. We also demonstrate operation with four ¹¹⁵In⁺ clock ions, which reduces the instability to 9.2×10⁻¹⁶/√τ/1\;s.