Sisyphus cooling

In ultra-low-temperature physics, Sisyphus cooling, the Sisyphus effect, or polarization gradient cooling involves the use of specially selected laser light, hitting atoms from various angles to both cool and trap them in a potential well, effectively rolling the atom down a hill of potential energy until it has lost its kinetic energy.

This cooling method was first proposed by Claude Cohen-Tannoudji in 1989,[1] motivated by earlier experiments which observed sodium atoms cooled below the Doppler limit in an optical molasses.

[2] Cohen-Tannoudji received part of the Nobel Prize in Physics in 1997 for his work.

The technique is named after Sisyphus, a figure in the Greek mythology who was doomed, for all eternity, to roll a stone up a mountain only to have it roll down again whenever he got it near the summit.

Sisyphus cooling can be achieved by shining two counter-propagating laser beams with orthogonal polarization onto an atom sample.

Atoms moving through the potential landscape along the direction of the standing wave lose kinetic energy as they move to a potential maximum, at which point optical pumping moves them back to a lower energy state, thus lowering the total energy of the atom.

(left-hand circularly polarized light), linear, and

(right-hand circularly polarized light) along the standing wave.

Note that this counter propagation does not make a standing wave in intensity, but only in polarization.

At positions where the counter-propagating beams have a phase difference of

In the intermediate regions, there is a gradient ellipticity of the superposed fields.

Consider, for example, an atom with ground state angular momentum

In the field-free case, all of these energy levels for each J value are degenerate, but in the presence of a circularly polarized light field, the Autler-Townes effect, (AC Stark shift or light shift), lifts this degeneracy.

The extent and direction of this lifted degeneracy is dependent on the polarization of the light.

It is this polarization dependence that is leveraged to apply a spatially-dependent slowing force to the atom.

In order to have a cooling effect, there must be some dissipation of energy.

Selection rules for dipole transitions dictate that for this example,

with relative intensities given by the square of the Clebsch-Gordan coefficients.

Suppose we start with a single atom in the ground state,

excited state, where it spontaneously emits a photon and decays to the

light, the AC stark shift lowers the

approximately equal to the AC Stark shift

where omega is the Rabi frequency and delta is the detuning.

state that it was pumped into, now experiences the opposite AC Stark shift as it did in

excited state, where it spontaneously emits a photon and decays to the

As before, this energy level has been lowered by the AC Stark shift, and the atom loses another

The fundamental lower limit of Sisyphus cooling is the recoil temperature,

, set by the energy of the photon emitted in the decay from the J' to J state.

though practically the limit is a few times this value because of the extreme sensitivity to external magnetic fields in this cooling scheme.

Atoms typically reach temperatures on the order of

Physical principle of Sisyphus cooling : The atoms are running against the potential energy, become excited into a higher band, fall back into a low-energy state (i.e. from the rather high "blue" state upwards, then immediately backwards to the lower "red" state), always on the left-hand side, from which, after one and a half of the "red" or "blue" period, say, of the laser action, they get excited and de-excited again, now from "red" to "blue", on the r.h.s., etc.