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

2 2 P 3/2
D 2=670.977nm
2 2 S 1/2
m J=+3/2
m J=+1/2
m J=-1/2
m J=-3/2
σ — transions
for imaging
m J=+1/2
m J=-1/2
Figure 7.43: Imaging transitions at high magnetic field.
The quantization axis is defined by the magnetic field orientation of the Feshbach
coils, which is chosen along the ˆz-axis. To take advantage of the maximum scattering
cross section the imaging beam would have to be σ − polarized and traveling along the
quantization axis. Unfortunately, this axis is reserved for doing the laser culling and
single atom detection, and imaging along this axis is therefore not easily implemented.
The imaging axis is perpendicular to the quantization axis instead. Because this axis is
also used for a MOT beam and MOT and imaging beam share optics, the imaging beam
is circularly polarized with opposite handedness than the MOT beam. Because of these
complications the full vector nature of the field amplitude E has to be considered [109].
in figure 7.44.
The calculations are performed in a rotated (primed) coordinate system as shown
In the lab frame the polarization of the atomic transition is given by σ − =
1/ √ 2(ˆx−iˆy). In the primed coordinate system the transition is hence σ−′ = 1/ √ 2(ˆx ′ −
iˆz ′ ). The scattering cross section, as will be shown below, is independent on the handed-
ness of the incident polarization, σ + or σ − polarized, and the handedness will therefore
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