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

7.5.1 Absorption Imaging
Determining the absorption scattering cross section in the case of lithium, espe-
cially in the presence of external magnetic fields, is not as straight forward as it is for
rubidium. The excited states are not resolved, thus making the two-level assumption
used to calculate the scattering cross-section invalid. In addition the existence of the
second hyperfine ground state cannot be neglected.
7.5.1.1 Absorption Scattering Cross Section at Zero Magnetic Field
For imaging the atoms at zero magnetic field, for example for measuring the
temperature of the MOT, both MOT and repump light are required. Without repump
light, the atoms will only scatter a few photons and then fall into the lower state, where
they are transparent to the MOT light. The absorption imaging beam used at zero
magnetic field is thus derived from the tapered amplifier, which has both MOT and
Repump frequencies.
In a multi-level atom, the on-resonance scattering cross section will differ from
the two-level approximation (σ0 = 3λ2),
and all possible transitions have to be taken
2π
into account. The transition matrix element is given by
µ = 〈(J2I)F2mF2|ˆµ(1,q)|(J1I)F1mF1〉, (7.1)
where the subscript 1 corresponds to the ground state, the subscript 2 to the excited
state respectively.
In lithium the excited state energy levels are degenerate to within the transition
linewidth, so all possible values for F2 have to be taken into account. The transition
matrix element will be shown to be independent of the polarization of the laser light,
and a random mixture of polarizations is therefore assumed. In addition, the magnetic
sublevels of the ground state will be mixed. An even mixture of these states is assumed
in the following calculation.
ê =
a(q)êq
q
(7.2)
|a(q)| 2 = 1. (7.3)
q
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