Single-Photon Atomic Cooling - Raizen Lab - The University of ...

process repeats. If however, it decays into the |J = 1/2,mJ = 1/2〉 state then
it is trapped in a cycling transition and has no way of returning to the |J =
1/2,mJ = −1/2〉 state. Note that the atom initially in the |J = 1/2,mJ =
−1/2〉 state climbed a potential hill to reach the region of σ + polarization
where it was optically pumped into the |J = 1/2,mJ = 1/2〉 state which has
lower energy due to a larger downward light shift. The atom therefore lost
the energy it used to climb the potential hill when it was transfered into the
other ground state. This excess energy is carried away by the spontaneously
emitted photon which has a higher frequency than the photon which excited
the atom into the J ′ = 3/2 manifold. After decay, the atom finds itself at the
bottom of a potential valley in the |J = 1/2,mJ = 1/2〉 state. If it climbs to
the top of this potential valley it will be in a region of σ − polarization and
will be pumped into the |J = 1/2,mJ = −1/2〉 state losing more energy in the
process. This repeated cycle of climbing a potential hill only to be pumped
into a valley is called the ‘Sisyphus’ effect after a character in Greek mythology
condemned by the gods to a similar fate.
This simple picture suggests that this cooling mechanism works until
the atoms no longer have sufficient energy to climb the potential hills and are
stuck in the valleys. A final temperature can be estimated with this picture
in mind [70]
kBT ≈ Udip ∝ I
. (2.83)
|∆|
where Udip can be estimated from Eq. 2.53. Of course this technique also
has a limit and cannot be used to cool atoms to 0 K as ∆ → 0 . When the
63