Quench dynamics of a superfluid Fermi gas

Abstract

With an eye toward the interpretation of so-called 'cosmological' experiments performed on the low-temperature phases of {sup 3}He, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter {lambda}. In {sup 3}He, the quenches induced by the rapid cooling of the 'hot spots' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap {delta}{sub {infinity}}={epsilon}{sub C}(e{sup 2/N(0){lambda}}-1){sup -1/2}. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.