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

We recently reported a Ca-40(+) optical clock comparison with an uncertainty at 5.5 x 10(-17), mainly limited by the excess micromotion shift. Here we report the progress made to reduce this shift and its uncertainty below 1 x 10(-18) by precise measurement of the "magic" rf drive frequency Omega(0) at which the micromotion-induced scalar Stark shift and second-order Doppler shift cancel each other. Omega(0) is measured as 2 pi x 24.801(2) MHz, and the differential static scalar polarizability Delta alpha(0) of the Ca-40(+) ion clock transition is measured as -7.2677(21) x 10(-40) J m(2) 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 x 10(-19) level. With further improvements made to reduce the servo error, the total clock uncertainty is reduced to 2.2 x 10(-17), limited by the blackbody radiation field evaluation.