Theory of adiabatic cooling in cavities

We analyze how a decaying cavity field can lead to significant atomic cooling. This cooling can be intuitively understood by invoking the adiabatic theorem to characterize the dynamics of an atom dressed by a classical field. We find numerically that cooling can proceed well into the quantum regime where there are only a few photons left in the cavity, and where the adiabatic theorem ceases to be applicable. A physical interpretation of this final cooling stage is given.