Resonance superfluidity in a quantum degenerate Fermi gas

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. This is related to the phenomenon of superconductivity described by the seminal Bardeen-Cooper-Schrieffer (BCS) theory. In superconductivity, the phase transition is caused by a coupling between pairs of electrons within the medium. This coupling is perturbative and leads to a critical temperature Tc which is small compared to the Fermi temperature TF. Even high-Tc superconductors typically have a critical temperature which is two orders of magnitude below TF. Here we describe a resonance pairing mechanism in a quantum degenerate gas of potassium (40K) atoms which leads to superfluidity in a novel regime--a regime that promises the unique opportunity to experimentally study the crossover from the BCS phase of weakly-coupled fermions to the Bose Einstein condensate of strongly-bound composite bosons. We find that the transition to a superfluid phase is possible at the high critical temperature of about 0.5TF. It should be straightforward to verify this prediction, since these temperatures can already be achieved experimentally.