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

to capturing atoms away from their classical turning points (see Eq. 1.3 and
related discussion). But this is not the case here because we are well into the
adiabatic regime: 〈τB〉/tramp ≈ 5 × 10 − 3 ≪ 1. Indeed, we estimate the energy
due to capturing atoms away from there classical turning points to be only
≈ 0.5µK. This excess energy can be explained by noting that this process only
cools the magnetically trapped atoms along the vertical dimension. Atoms
transfered into the optical trap retain their horizontal velocity, and due to the
geometry of the optical trough, energy in the y dimension is quickly mixed
with the z dimension, accounting for the non-vanishing T (z)
O .
The measure of the effectiveness of the single-photon cooling process
is the amount of phase space compression it produces. For a given initial
phase-space density, the compression is maximized when the final phase-space
density is maximized. Here we define the phase-space density of our atomic
ensembles in the usual manner [23]
ρ = nλ 3
h
d = n
(2πMkBT) 1/2
3
∝ nT −3/2 , (4.4)
where n is the atom number density and λd is the thermal de Broglie wave-
length. The point on Fig. 4.25 corresponding to the highest phase-space den-
sity is located at hp = 41µm.
We now come to the issue of addressing transfer efficiency from the
magnetic trap into the optical trough. To do this we compare the transfer
efficiency of the single-photon cooling process to the maximum transfer effi-
ciency expected in an adiabatic process transferring atoms between the two
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