Where Δ Δ 0 ′ is the light shift for the m F = 0 state. There is a motion induced population imbalance in the Zeeman sublevels in the z basis. For red detuned light, Δ Δ 0 ′ is negative, and thus there will be a higher population in the | g , m f = − − 1 ⟩ ⟩ state when the atom is moving to the right (positive velocity) and a higher population in the | g , m f = 1 ⟩ ⟩ state when the atom is moving to the left (negative velocity). From the Clebsch-Gordan coefficients, we see that the | g , m f = − − 1 ⟩ ⟩ state has a six times greater probability of absorbing a σ σ − − photon moving to the left than a σ σ + photon moving to the right. The opposite is true for the | g , m f = 1 > state. When the atom moves to the right it is more likely to absorb a photon moving to the left and likewise when the atom moves to the left it is more likely to absorb a photon moving to the right. Thus there is an unbalanced radiation pressure when the atom moves which dampens the motion of the atom, lowering its velocity and therefore its temperature.