Ca+40 ion optical clock with micromotion-induced shifts below 1×10−18

Abstract

We recently reported a $^{40}{\mathrm{Ca}}^{+}$ optical clock comparison with an uncertainty at $5.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$, mainly limited by the excess micromotion shift. Here we report the progress made to reduce this shift and its uncertainty below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ by precise measurement of the ``magic'' rf drive frequency ${\mathrm{\ensuremath{\Omega}}}_{0}$ at which the micromotion-induced scalar Stark shift and second-order Doppler shift cancel each other. ${\mathrm{\ensuremath{\Omega}}}_{0}$ is measured as $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}24.801(2)\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and the differential static scalar polarizability $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{0}$ of the $^{40}{\mathrm{Ca}}^{+}$ ion clock transition is measured as $\ensuremath{-}7.2677(21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\phantom{\rule{0.28em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}2}$. 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 $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ level. With further improvements made to reduce the servo error, the total clock uncertainty is reduced to $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$, limited by the blackbody radiation field evaluation.