Experiments with Supersonic Beams as a Source of Cold Atoms

of the laser itself, and the limits in reducing this broadening are discussed along with
the planned laser to produce 243 nm light. There are also two important sources of
inhomogeneous broadening which will play an important role, both in detecting the
atoms, and in setting resolution limits for spectroscopy of hydrogen isotopes in the
magnetic trap.
The first source of inhomogeneous broadening is transit time broadening, which
results from the time energy uncertainty relationship ΔEΔt >. An atom moving
through a laser beam will see the beam for a finite period of time, placing limits on the
energy resolution that can be observed. This broadening mechanism is inhomogeneous
because the amount of time an atom spends in the beam depends on each atom’s
trajectory, and so only the average broadening, related to the temperature of the
atoms in the sample, can be calculated. The width of the transit time broadening
for a sample at a specific temperature will vary as 1/ω0, whereω0 is the beam waist.
This means that decreasing the beam waist will increase the transit time broadening,
lowering the transition rate.
Given a fixed power in the laser, decreasing the waist will increase intensity,
making the transition rate go as ω −4
0 , while transit time broadening affects the rate
as ω0. The number of trapped atoms which pass through the beam also goes as
ω0, leading to an overall dependance of ω −2
0 . One technique for obtaining maximum
energy resolution for spectroscopy is to balance the laser linewidth broadening with
the transit time broading by picking a beam waist that makes their contributions
equal.
The final source of broadening that must be considered is the inhomogeneous
broadening due to the magnetic field of the trapping potential. While the Zeeman shift
of the 1S and 2S states both scale linearly with the magnetic field, there are relativistic
effects which introduce broadening. Specifically, there is a relativistic correction to
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