Experiments with Supersonic Beams as a Source of Cold Atoms

atom or molecule in a low-field-seeking state moves from a region of low field to a
region of high field, its potential energy increases. Since force F = −∇U where U
is the potential energy, a spatially varying magnetic field produces a force, and a
low-field-seeking atom or molecule is repelled from regions of high field. Conservation
of energy dictates that a particle loses kinetic energy equal to its gain in potential
energy. Thus, as a low-field-seeking atom enters a region of high field it will lose a
kinetic energy equivalent to the Zeeman shift of the internal states. For a particle
moving in an electromagnetic coil, the loss of kinetic energy T in the Zeeman regime
(assuming L − S coupling) is
ΔT = −μBgJmJΔB, (4.29)
and similarly in the Paschen-Back regime the change in kinetic energy is
ΔT = −μB (2mS + mL)ΔB. (4.30)
While a low-field-seeking particle loses kinetic energy moving from a region of
low field to a region of high field, the reverse is also true. Hence, a low field seeking
particle moving in an electromagnetic coil loses energy as it enters the coil, and if the
field is unchanged it regains the kinetic energy as it exits the coil. However, if the coil
is switched off quickly while the particle is in a region of high field, the particle loses
kinetic energy. This process can be repeated through multiple coils, each removing
kinetic energy from the beam, until the desired velocity is attained. The slowing
sequence for a single coil is illustrated in figure 4.5.
While equations 4.29 and 4.30 are exact for an ideal coil that switches instan-
taneously, a real coil is more complicated. In a real coil, the magnetic field turns
off over some period of time, during which the particle will continue to move in the
coil. For this reason, it is important to optimize the coil and switching electronics
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