Self-consistent theory of atomic Fermi gases with a Feshbach resonance at the superfluid transition

A self-consistent theory is derived to describe the BCS–Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and “bare” Feshbach molecules, has been included within a selfconsistent T-matrix approximation, beyond the Nozières and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature Tc increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor Zm of the molecule’s Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at Tc. Our many-body calculations of Zm agree qualitatively well with recent measurments of the gas of Li atoms near the broad resonance at 834 G. The crossover from narrow to broad resonances has also been studied.