The induced interaction in a Fermi gas with a BEC-BCS crossover

TL;DR

This paper investigates how induced interactions affect the superfluid transition temperature across the BEC-BCS crossover in a Fermi gas, extending existing theories and quantifying the impact at various interaction regimes.

Contribution

The study extends the Gorkov-Melik-Barkhudarov theory to the entire BEC-BCS crossover and incorporates pairing fluctuations using Nozières and Schmitt-Rink's approach.

Findings

Induced interaction reduces transition temperature by ~20% at unitarity.

Transition temperature decreases by a factor of about 2.22 in the BCS limit.

Induced interaction significantly impacts superfluid transition temperatures across the crossover.

Abstract

We study the effect of the induced interaction on the superfluid transition temperature of a Fermi gas with a BEC-BCS crossover. The Gorkov-Melik-Barkhudarov theory about the induced interaction is extended from the BCS side to the entire crossover, and the pairing fluctuation is treated in the approach by Nozi\`{e}res and Schmitt-Rink. At unitarity, the induced interaction reduces the transition temperature by about twenty percent. In the BCS limit, the transition temperature is reduced by a factor about 2.22, as found by Gorkov and Melik-Barkhudarov. Our result shows that the effect of the induced interaction is important both on the BCS side and in the unitary region.