Magic wavelengths and other properties of Li for optical cooling and trapping*

Using first-principles calculations, we identify magic wavelengths $\lambda$ for the $2s-2p_{1/2}$, $2s-2p_{3/2}$, $2s-3p_{1/2}$, and $2s-2p_{3/2}$ transitions in Li. The $ns$ and $np_j$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Possible differences between the positions of magic wavelengths in $^6$Li and $^7$Li are investigated. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Trends of dynamic polarizabilities of the ground and $2p_j$, $3s$, and $3p_j$ states are investigated. Uncertainties of all recommended values are estimated. Implications of our results for optical cooling and trapping of Li are discussed.