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 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 T$\text{}_{c}$ which is small compared to the Fermi temperature T$\text{}_{F}$. Even high-T$\text{}_{c}$ superconductors typically have a critical temperature which is two orders of magnitude below T$\text{}_{F}$. Here we describe a resonance pairing mechanism in a quantum degenerate gas of potassium ($\text{}^{40}$ K) atoms which leads to superfluidity in a novel regime - a regime that promises the unique opportunity to experimentally study the cross-over from the Bardeen-Cooper-Schrieffer 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 0.5 T$\text{}_{F}$. It should be straightforward to verify this prediction, since these temperatures can already be achieved experimentally.