We recently reported a ${}^{40}{\mathrm{Ca}}^{+}$ optical clock comparison with an uncertainty at $5.5\times {10}^{-17}$, mainly limited by the excess micromotion shift. Here we report the progress made to reduce this shift and its uncertainty below $1\times {10}^{-18}$ by precise measurement of the “magic” rf drive frequency ${\mathrm{\Omega }}_0$ at which the micromotion-induced scalar Stark shift and second-order Doppler shift cancel each other. ${\mathrm{\Omega }}_0$ is measured as $2\pi \times 24.801\left(2\right)\mathrm{MHz}$, and the differential static scalar polarizability $\mathrm{\Delta }{\alpha }_0$ of the ${}^{40}{\mathrm{Ca}}^{+}$ ion clock transition is measured as $-7.2677\left(21\right)\times {10}^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$. The blackbody radiation shift is then calculated to be 0.37913(12) Hz at 300 K considering the dynamic correction. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature has been reduced to the $3\times {10}^{-19}$ level. With further improvements made to reduce the servo error, the total clock uncertainty is reduced to $2.2\times {10}^{-17}$, limited by the blackbody radiation field evaluation.

• Received 9 March 2018

DOI:https://doi.org/10.1103/PhysRevA.99.011401