  We theoretically investigate strong-coupling properties of an ultracold Fermi
gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being
coupled with two fermion baths. By developing a non-equilibrium strong-coupling
theory based on the combined $T$-matrix approximation with the Keldysh Green's
function technique, we show that the chemical potential bias applied by the two
baths gives rise to the anomalous enhancement of
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing fluctuations (although the
system has no spin imbalance), resulting in the re-entrant behavior of the
non-equilibrium superfluid phase transition in the BCS-unitary regime. These
pairing fluctuations are also found to anomalously enhance the pseudogap
phenomenon. Since various non-equilibrium phenomena have recently been measured
in ultracold Fermi gases, our non-equilibrium strong-coupling theory would be
useful to catch up this experimental development in this research field.
