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

At T = 0 the non-interacting fermions will fill the trap up to the Fermi-Energy EF = µ
EF = ¯ω (6N) 1/3 = kBTF. (2.41)
and the radius of the trapped degenerate cloud is given by
2EF
Ri =
m¯ω 2.
(2.42)
The Fermi-Dirac distribution implies that at low temperatures (T ≈ TF) the
lowest energy levels of the trap will be filled with almost unit probability. Deviations
from the maximum filling are most likely to occur in the energy levels close to the
Fermi-energy. In the absence of additional excitation mechanisms, for example scattered
photons, the lowest energy levels of the trap will remain filled, and the smaller the final
temperature, the smaller the likelihood of finding vacancies within the distribution.
2.12 Spectroscopy
The frequency of the (near-)resonant laser beams in the experiment have to be
very well controlled. Close to resonance even small changes have a big impact on the
scattering rate and scattering force. It is therefore necessary to lock the laser system
directly to a spectroscopic line.
The natural linewidths of the D2 transitions in alkali atoms are on the order of
a few MHz. Unfortunately this narrow linewidth will be smeared out to hundreds of
MHz by Doppler-broadening. The source of this broadening lies, as the name suggests,
in the Doppler-effect. Consider an atom moving with velocity v in the lab frame. In
the reference frame of this atom the laser frequency ω is shifted to ω ′ = ω − k · v.
This particular atom will thus absorb a photon with frequency ω ′ . In an ensemble of
atoms with a Maxwell-Boltzmann velocity distribution the natural linewidth will thus
be broadened due to the different velocities of the atoms of the ensemble [22, 44].
Fortunately, Doppler-free spectroscopy methods exist which suppress the effect
of Doppler-broadening.
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