Sisyphus cooling

Method

Sisyphus cooling is achieved by directing two counter-propagating laser beams with orthogonal polarization onto a sample of atoms. The counter-propagation of these orthogonally polarized lasers creates a standing wave in polarization, not in intensity, with a gradient between left-hand circularly polarized light, linear, and right-hand circularly polarized light along the standing wave. This gradient occurs over a length scale and repeats, mirrored about the y-z plane. At positions where the counter-propagating beams have a phase difference of a certain value, the polarization is circular; where there is no phase difference, the polarization is linear; in intermediate regions, there is a gradient ellipticity of the superposed fields. Atoms moving through this potential landscape along the direction of the standing wave lose kinetic energy as they move to a potential maximum. At that point, optical pumping moves them back to a lower energy state, lowering the total energy of the atom. For an atom with ground state angular momentum and excited state angular momentum, the sublevels are degenerate in the field-free case. In the presence of a circularly polarized light field, the Autler-Townes effect (AC Stark shift or light shift) lifts this degeneracy, with the extent and direction depending on the polarization of the light. Selection rules for dipole transitions dictate that for this example, certain transitions occur with relative intensities given by the square of the Clebsch-Gordan coefficients. Starting with a single atom in the ground state at a certain position with velocity in the +z direction, the atom is pumped to the excited state, where it spontaneously emits a photon and decays to a different ground state. The AC Stark shift lowers one ground state further in energy than the other, so the atom loses an amount of energy approximately equal to the AC Stark shift, where omega is the Rabi frequency and delta is the detuning.