Blackbody-radiation shift in the Sr optical atomic clock

We evaluated the static and dynamic polarizabilities of the $5s^2{}^1{S}_0$ and $5s5p{}^3{P}_0^o$ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5s^2{}^1{S}_0-5s5p{}^3{P}_0^o$ dc Stark shift measurement $\Delta \alpha =247.379\left(7\right)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1$\%$ uncertainty; $-$0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7$\%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.

Figure 1

The frequency-dependent polarizabilities of the Sr $5s^2{}^1{S}_0$ and $5s5p{}^3{P}_0^o$ states near the 813.4-nm magic wavelength. The frequency-dependent polarizabilities of the $5s5p{}^3{P}_0^o$ state shifted by $\pm$1$\%$ are shown to illustrate the sensitivity of the magic wavelength to this polarizability. The magic wavelength is marked with an arrow.