Ultracold atom superfluidity induced by the Feshbach resonance

We discuss the possible signatures of superfluidity induced by the Feshbach resonance in ultracold gas of fermion atoms. Approaching the phase transition from above there appear various manifestations of the gradually emerging order parameter, but yet the long range coherence is not established due to strong quantum fluctuations. The single particle excitation spectrum becomes gapped while at the same time the pair excitations are characterized by the narrow quasiparticle peak surrounded by the incoherent background. This quasiparticle shows up certain collective features such as the remnant of the "first sound" which at Tc spreads down to low momenta. Presence of this Goldstone mode is the most unambiguous proof for appearance of the superfluid state. We discuss how such mode can be detected experimentally.