Determination of Sr properties for a high-accuracy optical clock

Abstract

We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\times {10}^{-17}$ and below. In particular, we focused on ac polarizabilities of the $5s^2$ ${}^{1}S_0$ and $5s5p$ ${}^{3}P_0^o$ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the ${}^{1}S_0\text{−}{}^{3}P_0^o$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the ${}^{3}P_0^o$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the ${}^{3}P_0^o$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\times {10}^{-17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.