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

Blackbody radiation (BBR) shifts of the ³P₀-¹S₀ 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 10⁻¹⁸ fractional accuracy of the optical-lattice-based clocks. A peculiarity of these clocks is that the characteristic BBR wavelength is comparable to the ³P 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 10⁻¹⁸ accuracy goal.