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

ight and polarized along ˆx superposes with a beam traveling in the oppo-
site direction polarized along ˆy. The local polarization depends on the rel-
ative phase difference between the two beams and varies from σ + to σ − in
a distance ∆z = λ/4. This polarization gradient causes a spatial, periodic
modulation of the energy of each of the ground states |J = 1/2,mJ = 1/2〉
and |J = 1/2,mJ = −1/2〉 of different magnitude given roughly by Eq. 2.53.
For example, consider a location at which the local polarization is σ + . If
the laser beams are tuned below the atomic resonance frequency then both
ground states will be shifted downwards in energy, however because the cou-
pling between the |J = 1/2,mJ = 1/2〉 and |J = 3/2,mJ = 3/2〉 state is
stronger, this ground state is shifted downward more. Conversely, at locations
where the light has σ − polarization the ground state |J = 1/2,mJ = −1/2〉 is
shifted downward in energy more. These two states oscillate in energy along
the polarization gradient as shown in Fig. 2.9(c).
If these energy level shifts (known as light shifts) were the only effect
the light had on the atoms then we would expect the atoms to exchange
potential and kinetic energy as they traveled over the potential hills, but we
would not expect any further cooling to take place due to the light. However
the light does effect the atoms in another way, it optically pumps them in
a spatially dependent way. For example, consider what happens to an atom
initially in the |J = 1/2,mJ = −1/2〉 state located at a position with σ + light
polarization. After being excited into the |J = 3/2,mJ = 1/2〉 state it has
two modes of decay. If it decays back into the |J = 1/2,mJ = −1/2〉 state the
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