We report a single-ion optical clock based on the $4S_{1/2}\to 3D_{5/2}$ transition of the ${}^{40}{\mathrm{Ca}}^{+}$ ion, operated in a liquid nitrogen cryogenic environment, achieving a total systematic uncertainty of $4.4\times {10}^{-19}$. We employ a refined temperature evaluation scheme to reduce the frequency uncertainty due to blackbody radiation, and 3D sideband cooling to minimize the second-order Doppler shift. We have precisely determined the average Zeeman coefficient of the ${}^{40}{\mathrm{Ca}}^{+}$ clock transition to be $14.345(15)\mathrm{Hz}/{\mathrm{mT}}^2$, thereby significantly reducing the quadratic Zeeman shift uncertainty. Moreover, the cryogenic environment enables the lowest reported heating rate due to ambient electric field noise in trapped-ion optical clocks.

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• Atom & ion cooling
• Atom & ion trapping & guiding
• Atomic & molecular processes in external fields
• Atomic, optical & lattice clocks