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

assume that l1 >> l2 and that the action of the one-way-wall heats the en-
semble only a negligible amount then the phase-space compression C achieved
is given simply by
C ≡ ρafter
ρbefore
≈ l1
l2
(1.2)
While instructive, this simple example is clearly unphysical. The action
of the barrier violates time reversal symmetry! Additionally, we have gotten
something, namely atomic cooling, for nothing – in clear violation of the second
law of thermodynamics. The resolution of these troubling facts comes from
recognition that any physical realization of an atomic one-way-wall must affect
the atoms beyond simply transmitting or reflecting them. For the action of the
one-way-wall as presented thus far to obey time reversal symmetry the atoms
on the left of the wall must be different in some way from the atoms on the
right of the wall. Additionally, the decrease in entropy produced through the
action of the one-way-wall must be compensated for by an increase in entropy
elsewhere if this scheme is to obey the second law of thermodynamics. Indeed,
in the physical realization of this cooling process presented in this dissertation
the one-way-wall labels the atoms on either side of the barrier by placing them
into distinct hyperfine states through an irreversible spontaneous scattering
process of a single photon as atoms transit the barrier. This scattering process
is of course the origin of the name “single-photon cooling.” Much more will
be said of this in Ch. 4 where a complete description of the cooling process
applied to 87 Rb is described.
Now consider a second example, a slight variation of the first, which
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