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

5.2 Branching Ratios and Population Distribution
The irreversible step in the implementation of single-photon cooling in rubidium
lies in the spontaneous scattering event that occurs after the atom has been excited to the
|F ′ = 1〉 state. Because of the branching ratios it is impossible to transfer all the atoms
from the |F = 2,mF = 2〉 state into one final trapped state in the gravito-optical trap.
Instead they are evenly distributed between the |F = 1,mF = 1〉 and |F = 1,mF = 0〉
states. After completion of the single-photon cooling sequence, the distribution of atoms
between the two final states is determined by applying a magnetic field gradient such
that atoms in the |F = 1,mF = 1〉 state are ejected out of the gravito-optical trap,
leaving only the magnetically decoupled atoms in the |F = 1,mF = 0〉 state in the trap.
As expected about 50% of the total number of atoms are in this state. Only atoms in
the |F = 1,mF = 0〉 state are considered when calculating phase-space density.
About 10% of the atoms that encounter the demon will fall back into the |F =
2,mF = 2〉 state, and about 5% will fall into the |F = 2,mF = 1〉 state. These atoms
are thus transferred back into the reservoir and can undergo another cycle of excitation
and decay when encountering the demon beam. Only about 5% of the atoms decay into
the untrapped |F = 2,mF = 0〉 state and are lost from the system.
5.3 Effect of the Demon Beam Detuning
As mentioned before, the demon beam is slightly detuned from resonance. Naively
one would assume that the beam should ideally be on resonance. This is not true, as
figure 5.5 shows. The maximum number of atoms is transferred into the trough not at
zero detuning, but rather at a power-dependent optimum value.
There are two reasons for this phenomenon. First, consider the scattered photon.
As the density of atoms in the trap increases, the probability of reabsorption of this
photon by atoms in the optical trough increases as well. If this photon is absorbed by
an atom inside the trap, this additional scattering event can lead to trap loss. If the
demon beam detuning ∆ is away from resonance, the probability of reabsorption of this
photon is dramatically decreased, as the scattering rate is roughly proportional to 1/∆.
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