$^{171}$Yb$^+$ optical clock with $2.2\times 10^{-18}$ systematic uncertainty and absolute frequency measurements

A full evaluation of the uncertainty budget for the ytterbium ion optical clock at the National Physical Laboratory (NPL) was performed on the electric octupole (E3) $^2\mathrm{S}_{1/2}\,\rightarrow\, ^2\mathrm{F}_{7/2}$ transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of $2.2\times 10^{-18}$. Furthermore, the absolute frequency of the E3 transition of the $^{171}$Yb$^+$ ion was measured between 2019 and 2023 via a link to International Atomic Time (TAI) and against the local caesium fountain NPL-CsF2. The absolute frequencies were measured with fractional standard uncertainties between $3.7 \times 10^{-16}$ and $1.1 \times 10^{-15}$, and all were in agreement with the 2021 BIPM recommended frequency.