  Non-equilibrium stimulation of superfluidity in trapped Fermi gases is
discussed by analogy to the work of Eliashberg [G. M. Eliashberg, in
"Nonequilibrium Superconductivity," edited by D. N. Langenberg and A. I. Larkin
(North-Holland, New York, 1986)] on the microwave enhancement of
superconductivity. Optical excitation of the fermions balanced by heat loss due
to thermal contact with a boson bath and/or evaporative cooling enables
stationary non-equilibrium states to exist. Such a state manifests as a shift
of the quasiparticle spectrum to higher energies and this effect effectively
raises the pairing transition temperature. As an illustration, we calculate the
effective enhancement of Cooper pairing and superfluidity in both the normal
and superfluid phases for a mixture of Rb and Li in the limit of small
departure from equilibrium. It is argued that in experiment the desirable
effect is not limited to such small perturbations and the effective enhancement
of the pairing temperature may be quite large.
