Sisyphus cooling
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Sisyphus.svg/220px-Sisyphus.svg.png)
In ultra-
Method
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. This description of Sisyphus cooling is largely based on Foot's description. [3]
Principle of Sisyphus cooling
The counter-propagation of two orthogonally polarized lasers generates a standing wave in polarization with a gradient between (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. This gradient occurs over a length scale of , and then repeats, mirrored about the y-z plane. At positions where the counter-propagating beams have a phase difference of , the polarization is circular, and where there is no phase difference, the polarization is linear. In the intermediate regions, there is a gradient ellipticity of the superposed fields.
Consider, for example, an atom with ground state angular momentum and excited state angular momentum . The sublevels for the ground state are
and the levels for the excited state are
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
Typical optical pumping scheme
In order to have a cooling effect, there must be some dissipation of energy. Selection rules for dipole transitions dictate that for this example, and with relative intensities given by the square of the
The atom is now pumped to the excited state, where it spontaneously emits a photon and decays to the ground state. The key concept is that in the presence of light, the AC stark shift lowers the further in energy than the state. In going from the to the state, the atom has indeed lost in energy, where approximately equal to the AC Stark shift where omega is the Rabi frequency and delta is the detuning.
At this point, the atom is moving in the +z direction with some velocity, and eventually moves into a region with light. The atom, still in its state that it was pumped into, now experiences the opposite AC Stark shift as it did in - light, and the state is now lower in energy than the state. The atom is pumped to the excited state, where it spontaneously emits a photon and decays to the state. As before, this energy level has been lowered by the AC Stark shift, and the atom loses another of energy.
Repeated cycles of this nature convert kinetic energy to potential energy, and this potential energy is lost via the photon emitted during optical pumping.
Limits
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. This limit is 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 , as compared to the doppler limit .
References
- .
- PMID 10039050.
- ISBN 9780198506966.
- Metcalf, Harold J.; van der Straten, Peter (1999). Laser Cooling and Trapping. Springer. Section 8.8. ISBN 9780387987286.
- "intro_Eng". Lkb.ens.fr. Retrieved 2009-06-05.