Dynamic polarizabilities and triple magic trapping conditions for $5s^2{}^1{S}_0\to 5s5p{}^3{P}_{0,2}$ transitions of Cd atoms

The dynamic electric dipole polarizabilities of the $5s^2{}^1{S}_0$, $5s5p{}^3{P}_0$, and $5s5p{}^3{P}_2$ states for Cd atoms are calculated using the relativistic configuration interaction plus many-body perturbation theory method. The magic wavelengths for the $5s^2{}^1{S}_0\to 5s5p{}^3{P}_0$ and $5s^2{}^1{S}_0\to 5s5p{}^3{P}_2$ transitions within a range of 300-500 nm are identified. The possibility of achieving triple magic trapping for the transitions $5s^2{}^1{S}_0\to 5s5p{}^3{P}_0$ and $5s^2{}^1{S}_0\to 5s5p{}^3{P}_2$ is investigated. It is found that no common magic wavelength could be identified for achieving triple magic trapping with the linearly polarized light. However, if the degree of ellipticity is between $0.358$ and $1$, the triple magic trapping can be achieved at 419.88 nm for the $5s^2{}^1{S}_0\to 5s5p{}^3{P}_2$ ($M_i=\pm 2$) and $5s^2{}^1{S}_0\to 5s5p{}^3{P}_0$ transitions.