Choosing the polarization in the rotating frame to be fixed along y ^ ^ , the unperturbed atomic eigenstates are the eigenstates of F ^ ^ y . The rotating term in the Hamiltonian causes perturbations in the atomic eigenstates such that the Zeeman sublevels become contaminated by each other. For F g = 1 the | g , m f = 0 ⟩ ⟩ y is light shifted more than the | g , m f = ± ± 1 ⟩ ⟩ y states. Thus the steady state population of the | g , m f = 0 ⟩ ⟩ y is higher than that of the other states. The populations are equal for the | g , m f = ± ± 1 ⟩ ⟩ y states. Thus states are balanced with ⟨ ⟨ F ^ ^ y ⟩ ⟩ = 0 . However, when we change basis we see that populations are not balanced in the z-basis and there is a non-zero value of ⟨ ⟨ F ^ ^ z ⟩ ⟩ proportional to the atom's velocity: