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

Xia-Ji Liu, Hui Hu
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
A self-consistent theory is derived to describe the BCS-BEC 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 self-consistent $T$-matrix approximation, beyond the Nozi\'{e}res and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the
more » ... o investigate the normal state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature $T_c$ increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor $Z_m$ of the molecule's Green function and a complex effective mass have been determined, to characterize the fraction and lifetime of Feshbach molecules at $T_c$. Our many-body calculations of $Z_m$ agree qualitatively well with the recent measurments on the gas of $^6$Li atoms near the broad resonance at 834 Gauss. The crossover from narrow to broad resonances has also been studied.
doi:10.1103/physreva.72.063613 fatcat:m6q55wgswngdbh7ryt7bhaqqzm