Higher-order lattice light shifts in the Cd optical clock

The $5s^2\,^1\!S_0 -\, 5s5p\, ^3\!P^o_0$ transition in cadmium is an attractive candidate for an optical lattice clock because it allows for an efficient narrow-line cooling and has a small sensitivity to blackbody radiation~[1], the effect which dominates the uncertainty budget of Sr and Yb clocks. Two isotopes of Cd have a nuclear spin of 1/2, which precludes tensor light shifts from the lattice light, another advantageous feature. In this work we address the problem of higher-order lattice light shifts in the Cd clock caused by the multipolar $M1$ and $E2$ atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. Using the method that combines configuration interaction and linearized coupled-cluster single double method we found the magnetic dipole and electric quadrupole polarizabilities and hyperpolarizabilities at the magic wavelength of the $^1\!S_0$ and $^3\!P^o_0$ states and determined these quantities for the clock transition frequency. The results are compared with those for the $5s^2\,^1\!S_0 -\, 5s5p\, ^3\!P^o_0$ Sr clock transition. \\ \noindent [1] A.~Yamaguchi, M.~S.~Safronova, K.~Gibble, and H.~Katori, Phys. Rev. Lett. {\bf 123}, 113201 (2019)