To see the relation between polarization and light shift, we look at the transition probabilities (Clebsch-Gordon coefficients squared) in a simple J=1/2 → J=3/2 transition (Figure 3).

The ground state has two sublevels (labelled  g_-1/2  and  g_1/2 , in which m=-1/2 and m=1/2, respectively). There are three possible transitions out of each sublevel: Δm = +1,0,-1 corresponding to absorption of a σ⁺, linear, or σ^- polarized photon. The transitions out of a given sublevel have differing Clebsch-Gordon coefficients and thus the light shift that the level experiences depends on the polarization of the local light field.