Dynamic polarizabilities and triple magic trapping conditions for 5s²~¹S₀→ 5s5p~³P0,2 transitions of Cd atoms

The dynamic electric dipole polarizabilities of the 5s²~¹S₀, 5s5p~³P₀, and 5s5p~³P₂ states for Cd atoms are calculated using the relativistic configuration interaction plus many-body perturbation theory method. The magic wavelengths for the 5s²~¹S₀→ 5s5p~³P₀ and 5s²~¹S₀→ 5s5p~³P₂ transitions within a range of 300-500 nm are identified. The possibility of achieving triple magic trapping for the transitions 5s²~¹S₀→5s5p~³P₀ and 5s²~¹S₀→5s5p~³P₂ 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 5s² ~ ¹S₀→ 5s5p~³P₂ (Mᵢ=±2) and 5s²~¹S₀→5s5p~³P₀ transitions.