Effect of Laser Cooling on Frequency Standard of Single Ca⁺ Ion Trapped in a Radio-Frequency Paul Trap

The source of systematic frequency shift of single-ion optical frequency standard of ⁴⁰Ca⁺ ion trapped in endcap trap and laser-cooled to a few of mK is analysed and calculated. Second-order Doppler shift, Stark shift due to micromotion and thermal motion, blackbody Stark shift and ac Stark shift are calculated for the ground state and excited 3d ²D_5/2 state. The Hertz-level measurement of the optical clock frequency in a single ⁴⁰Ca⁺ ion can be performed.