For the case of counterpropagating waves with orthogonal circular polarizations the resulting polarization is linear everywhere, but rotates about  at an angle . As a result, there is no Sisyphus effect. The rotating polarization instead leads to motion-induced population imbalances in the Zeeman levels that cause imbalances in radiation pressure leading to a damping of the atomic motion. These population imbalances are only present for states with  or higher.
Consider two EM waves detuned from an atomic transition  with equal amplitudes:  and . The superposition of these two waves is:
As previously stated, the polarization of the total field is linear, but rotated around  by an angle  with respect to .
Consider an atom moving along z with some velocity v. The atom sees the polarization rotating with a frequency of . In the rotating frame, the polarization is fixed, however, there is an inertial field due to the frame rotating. This inertial term appears in the Hamiltonian as follows.
Here we see the inertial term looks like a magnetic field along  with an amplitude such that the Larmor precession frequency is equal to rotation frequency in the lab frame. For small v, this term in Hamiltonian can be treated using perturbation theory.
Choosing the polarization in the rotating frame to be fixed along , the unperturbed atomic eigenstates are the eigenstates of . The rotating term in the Hamiltonian causes perturbations in the atomic eigenstates such that the Zeeman sublevels become contaminated by each other. For  the  is light shifted more than the  states. Thus the steady state population of the  is higher than that of the other states. The populations are equal for the  states. Thus states are balanced with . However, when we change basis we see that populations are not balanced in the z-basis and there is a non-zero value of  proportional to the atom's velocity:
Where  is the light shift for the  state. There is a motion induced population imbalance in the Zeeman sublevels in the z basis. For red detuned light,  is negative, and thus there will be a higher population in the  state when the atom is moving to the right (positive velocity) and a higher population in the  state when the atom is moving to the left (negative velocity). From the Clebsch-Gordan coefficients, we see that the  state has a six times greater probability of absorbing a  photon moving to the left than a  photon moving to the right. The opposite is true for the  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.
Note the similarity to Doppler cooling in the unbalanced radiation pressures due to the atomic motion. The unbalanced pressure in PG cooling is not due to a Doppler shift but an induced population imbalance. Doppler cooling depends on the parameter  where  is the scattering rate, whereas PG cooling depends on . At low intensity  and thus PG cooling works at lower atomic velocities (temperatures) than Doppler Cooling.