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

traps. If we model the ensembles in both the optical and magnetic trap with
Maxwell-Boltzmann velocity distributions and Gaussian spatial distributions
we can arrive at a simple analytical formula predicting the transfer efficiency
between the two traps via an adiabatic process. Strictly speaking, the mag-
netic and optical potentials are not harmonic, and therefore the assumption
of a Gaussian spatial distribution is clearly an approximation for our exper-
iment. However, we maintain this approximation because of the simplicity
and generality it affords our expression predicting the transfer efficiency. We
estimate that this assumption leads to an error of roughly 15%, which does
not affect the conclusions drawn from comparing the model with experiment.
Under an adiabatic transfer, the most atoms one could expect to transfer from
the large-volume, deep magnetic trap into the small-volume, shallow optical
trap is given by overlap of the the phase-space distribution of atoms in the
two traps. Under the assumptions given above, we may write this overlap as
η ≡ NO
=
NB
σ (i)
(i)
O T O
, (4.5)
i={x,y,z}
where NO (NB), σO (σB), and TO (TB) are the number, 1/e radius and tem-
perature of the atoms in the optical (magnetic) trap, respectively. In this for-
mula the product runs over all three orthogonal dimensions to allow for trap
σ (i)
B
T (i)
B
anisotropy. Furthermore, this form is only valid when (σ (i)
O
is true.
,T (i)
O
(i)
) ≤ (σ(i)
B ,T B )
Now we must consider the effect of single-photon atomic cooling on
the transfer process. In a non-interacting ensemble, the single-photon atomic
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