Experiments to Control Atom Number and Phase-Space Density in ...

ight side of the box. An irreversible step is required to break the time-reversal symmetry.
In addition, consider the effects of this process on the entropy. The decrease in entropy
of the trapped atoms must be compensated by an increase in entropy somewhere else.
Otherwise the second law of thermodynamics would be violated.
The entropy of an ideal gas is given by the Sackur-Tetrode equation
V 4πmU
S = NkB ln
N 3Nh2
3/2
+ 5
, (3.2)
2
where U is the internal energy of the gas, and h is Planck’s constant. The change in
entropy associated with the accumulation of atoms on the right hand side of the one-way
barrier is thus given by
Vi
∆S = Si −Sf = NkBln .
Vf
(3.3)
The answer to the question what happens to the entropy can be answered by looking at
the physical realization of the one-way wall barrier.
The required energy level structure for one possible realization of the one-way
wall is shown in figure 3.2 (c). This is the level structure of the alkali atoms, where
the ground state is split into two hyperfine states. The one-way wall itself consists of a
barrier beam, red-detuned for atoms in state |1〉, and blue-detuned for atoms in state |2〉.
Atoms in state |1〉 (red) can thus pass through the attractive potential of the barrier.
They then encounter a repump beam that pumps the atoms from state |1〉 (red) into
state |2〉 (blue). For atoms in state |2〉 the barrier beam provides a repulsive potential,
confining the atoms to the right hand side. This one-way wall scheme was realized and
studied in [57–59].
As the atoms pass through the one-way wall, each atom scatters one photon.
This photon is not only the irreversible step required to break time-reversal symmetry,
this photon also carries away the entropy, increasing the entropy of the radiation field.
3.3 Single-Photon Cooling
The amount of phase-space compression achievable with the one-way wall is lim-
ited by the trap volumes that are reasonable to use. More phase-space compression is
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