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

J=1
J=0
-1
Δ
σ + σ -
σ -
0
+1 -1 0 +1 0
-1
σ +
E z=z’
ω
σ + σ- σ + σ- m=+1
m=0
m=-1
m=0
+1
Figure 2.16: 1D magneto optical trap setup for the case of an atom with ground state
J = 0 and excited state J = 1. The quadrupole magnetic field causes a Zeeman splitting
of the excited state magnetic levels. At the position z = z ′ the |J = 0,m = 0〉 → |J =
1,m = −1〉 transition is resonantly driven by a laser with frequency ω = ω0 −∆. This
transition is driven by σ − circularly polarized light. This implies that the atom scatters
more photons from the beam coming from the right than from the beam coming from
the left, where the laser frequency is detuned by 2∆ from resonance. This imbalance in
scattering events forces the atom back towards the center of the trap.
The final form of the equation emphasizes the emergence of the restoring force due to
the imbalance in the number of scattering events caused by the Zeeman shift of the
energy levels.
Unfortunately neither rubidium nor lithium have a level structure as simple as
the one in the example above. Figures 2.17 and 2.18 show the energy level structure of
rubidium and lithium and the transitions used in the implementation of the magneto-
optical trap.
Even the relatively simple level structure of the alkali atoms does not offer a
completely closed cycling transition. Because the ground state consists of two hyperfine
states, a repump laser has to be added to the setup. This repump laser allows atoms
to be pumped back into the cooling cycle driven by the MOT transition. The necessary
strength of the repump light depends on the branching ratios. For rubidium the required
amount repump light is small, making it possible to use a single repump beam. Lithium
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