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

phase-space density is defined as ρ ≡ nλ3 dB , λdB = √ √ 2π , where n is the spatial density
mkBT
of atoms with mass m at temperature T. The phase-space density is limited by the
temperature achievable in a MOT as well as by the spatial density of atoms (typically
on the order of ≈ 10 11 cm −3 ) [38]. Once the density exceeds a critical value atoms
start absorbing fluorescent light emitted by other atoms. This leads to a repulsive force
between the atoms limiting the maximum density [35].
2.10 Evaporative Cooling
The phase-space density in a magneto-optical trap is still about 6 orders of mag-
nitude below degeneracy. The standard method of cooling alkali atoms further is evap-
orative cooling. This can happen in either a magnetic trap using an RF-knife, as is
typically done for 87 Rb or 23 Na, or in an optical dipole trap, as is typically done for
6 Li, where evaporative cooling in a magnetic trap is not possible, see chapter 2.5.1. The
basic principle of evaporative cooling is illustrated in figure 2.19.
Consider an atomic cloud trapped in an optical dipole trap of trap depth U. If
the thermal tail extends above the trap depth, the hottest atoms with E > U will leave
the trap, effectively lowering the average energy of the remaining atoms. The remaining
atoms then rethermalize through collisions, thus lowering the average temperature of the
trapped atoms. Both of these processes happen simultaneously, until the thermal tail
no longer extends above the trap depth and evaporation stops. The evaporative cooling
process can be forced to continue by reducing the trap depth U.
Evaporative cooling can only be applied successfully if elastic collisions between
atoms dominate over inelastic collisions. This is true for both fermions and bosons.
However, fermions cannot scatter with other fermions in the same state, due to the
anti-symmetric nature of their wavefunction. Evaporative cooling can therefore only be
done using either atoms in two different states [39], using two different atoms, or by
sympathetic cooling [14]. The condition of a dominating elastic cross section is satisfied
for the two lowest states of 6 Li, |F = 1/2,mF = 1/2〉 and |F = 1/2,mF = −1/2〉, and
it is therefore possible to use these states for evaporative cooling.
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