Single-Photon Atomic Cooling - Raizen Lab - The University of ...

cooling experiments, which are performed in ultrahigh vacuum environments,
the atomic ensemble being cooled is necessarily trapped optically and/or mag-
netically away from any thermal reservoir (e.g. the vacuum chamber walls).
While the atoms may be in a steady-state situation, they are not necessarily in
thermodynamic equilibrium. Despite this fact it is often convenient to define
the temperature of an ensemble of atoms as
1
2 kBT = 〈Ek〉 (1.5)
where kB is Boltzmann’s constant and 〈Ek〉 is the average kinetic energy of an
ensemble in 1-D.
It is also worth noting that throughout this text, cooling is used not
in the weak sense, as simply a reduction in temperature, but in a much more
meaningful way - as an increase in phase-space density. This distinction must
be made because an atomic vapor can always be trivially cooled through adia-
batic expansion, but this sort of “cooling” is rarely useful in experiments. For
most atomic physics experiments such as Bose-Einstein condensation or spec-
troscopic investigations of atomic energy structures, an increase in phase-space
density is what is helpful.
As mentioned above, atoms in these sorts of experiments are typically
trapped optically and/or magnetically and so a trapping depth is commonly
reported. In this context, trapping depth refers to the potential energy depth
of the trap (see Fig. 1.8). Atoms with total energy less than the trap depth
are considered trappable while those with energy greater than the trap depth
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