  We propose a pairing-based method for cooling an atomic Fermi gas. A three
component (labels 1, 2, 3) mixture of Fermions is considered where the
components 1 and 2 interact and, for instance, form pairs whereas the component
3 is in the normal state. For cooling, the components 2 and 3 are coupled by an
electromagnetic field. Since the quasiparticle distributions in the paired and
in the normal states are different, the coupling leads to cooling of the normal
state even when initially $T_{paired}\geq T_{normal}$ (notation $T_S\geq T_N$).
The cooling efficiency is given by the pairing energy and by the linewidth of
the coupling field. No superfluidity is required: any type of pairing, or other
phenomenon that produces a suitable spectral density, is sufficient. In
principle, the paired state could be cooled as well but this requires
$T_N<T_S$. The method has a conceptual analogy to cooling based on
superconductor -- normal metal (SN) tunneling junctions. Main differences arise
from the exact momentum conservation in the case of the field-matter coupling
vs. non-conservation of momentum in the solid state tunneling process.
Moreover, the role of processes that relax the energy conservation requirement
in the tunneling, e.g. thermal fluctuations of an external reservoir, is now
played by the linewidth of the field. The proposed method should be
experimentally feasible due to its close connection to RF-spectroscopy of
ultracold gases which is already in use.
