Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks

Abstract

Blackbody radiation (BBR) shifts of the $^{3}P_{0}\text{\ensuremath{-}}^{1}S_{0}$ clock transition in the divalent atoms Mg, Ca, Sr, and Yb are evaluated. The dominant electric-dipole contributions are computed using accurate relativistic many-body techniques of atomic structure. At room temperatures, the resulting uncertainties in the $E1$ BBR shifts are large and substantially affect the projected ${10}^{\ensuremath{-}18}$ fractional accuracy of the optical-lattice-based clocks. A peculiarity of these clocks is that the characteristic BBR wavelength is comparable to the $^{3}P$ fine-structure intervals. To evaluate relevant $M1$ and $E2$ contributions, a theory of multipolar BBR shifts is developed. The resulting corrections, although presently masked by the uncertainties in the $E1$ contribution, are required at the ${10}^{\ensuremath{-}18}$ accuracy goal.