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. We apply our theory to consider a specific resonance in potassium ( ${}^{40}\mathrm{K}$), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about ${0.5T}_F$. Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly coupled fermions to the Bose-Einstein condensation of strongly bound composite bosons.