Thus we now see that a spatially varying polarization in the light field will produce a spatially varying shift in the energy levels of atoms.  When analyzing the dynamics of atoms in an OL, we consider only the motion of the atoms in the ground state - the motion on the excited does not differ significantly from the ground state and thus it provides no addition information--so we ignore it.

Figure 4 illustrates the shift of the two ground states as a function of position caused by a red detuned light field (the circles serve as visual aides).

In the absence of a light field, the sublevels are degenerate.  When the atoms are in a position where the polarization is purely sigma plus, the g_-1/2  level is shifted down 3 times as far as the g_-1/2, because the transition probability is 3 times as great. Similar arguments apply when the polarization is linear and sigma minus, and thus the sublevels will vary periodically with position. When the OL is in steady state, the atoms will rest in the minima of these energy potentials.

In general, the precooled atoms are too energetic to be confined in these potentials, so they must be cooled even further, by a process known as Sisyphus cooling.