Experiments to Control Atom Number and Phase-Space Density in ...

Figure 5.8: Atom number as a function of trap depth.
Additionally, the optical trough truncates the spatial distribution along the x
and y directions. Figure 5.9 shows the number of atoms captured in the optical trough
as a function of the separation between the end caps. A larger trap volume leads to less
truncation and hence an increased number in the atoms captured from the ensemble.
This analysis shows that the final phase-space density is not necessarily the best
measure to evaluate the efficiency of single-photon cooling. The final phase-space density
measured is a three-dimensional quantity, while the cooling process in this implemen-
tation is only one-dimensional. To evaluate the vertical phase-space compression, it is
helpful to look at the transfer efficiency η from the magnetic trap to the optical trap,
η = NO
NB , NO is the atom number in the optical trough and NB the number of mag-
netically trapped atoms, and compare the measured values with the maximum values
expected from an adiabatic transfer process.
The model describing the adiabatic transfer is greatly simplified by approximating
the spatial distributions as Gaussian. The temperature distributions are assumed to
follow Maxwell-Boltzmann velocity distributions. Neither the magnetic nor the optical
trap provide harmonic potentials and thus the approximation of the spatial profile as
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