Experiments with Supersonic Beams as a Source of Cold Atoms

The apertures set the transverse temperature, and hotter atoms are removed from the
beam by the apertures, leaving only the colder atoms in the beam. For this reason,
it is appropriate to concentrate on the parallel component of the velocity, giving the
Gaussian velocity profile
m
p(v) = e
2πkBT
− m(v
−w) 2
2kB T
=
σ
1
√ e
2π −(v
−w) 2
2σ 2 , (2.25)
where σ is the standard deviation in the velocity parallel to the beam axis. This
velocity distribution is compared to the Maxwellian velocity distribution for a few
relevant gas species and reservoir temperatures in figure 2.1. As can be seen in
the figure, the width of the velocity profile is significantly narrower for the case of
a supersonic beam. Expressed in terms of temperature, beams of a few tens to a
few hundred milliKelvin are common. This is significantly colder than the reservoir
temperatures, and the supersonic expansion has effectively cooled the beam.
The cooling achieved by supersonic expansion is extremely general and can be
used to cool any desired species. In the above discussion on isotropic expansion, it is
assumed that the gases were truly ideal gases. Supersonic beams are generally created
with a noble carrier gas that generally behaves as an ideal gas at higher pressures
and lower temperatures than many other gas species. Other species of interest are
mixed in the reservoir before the expansion, or added just outside the nozzle during
the expansion. If the species of interest is a gas at the reservoir temperature, it is
typically seeded into the carrier gas in the reservoir. A species that is not a gas at the
reservoir temperature is typically entrained into the beam at the exit of the nozzle.
Laser ablation can be used to produce an atomic sample of a solid at the exit of a
nozzle, or alternatively, an oven can produce an atomic beam that is then entrained in
the supersonic beam. In either case, the added species is cooled by thermalizing with
the dominant carrier gas and is carried along with the supersonic beam, providing a
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