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

TL;DR

This paper develops a self-consistent theoretical framework for describing the BCS-BEC crossover in strongly interacting Fermi gases with Feshbach resonances, including molecule fluctuations and comparing results with experimental data.

Contribution

It introduces a self-consistent $T$-matrix approach that accounts for molecule fluctuations beyond previous models, providing detailed predictions for superfluid transition and molecule properties.

Findings

Superfluid transition temperature $T_c$ increases with interaction strength.

Residue factor $Z_m$ and effective mass characterize molecule fraction and lifetime.

Qualitative agreement with experimental measurements on $^6$Li near broad resonance.

Abstract

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 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.