The Contact in the BCS-BEC crossover for finite range interacting ultracold Fermi gases

TL;DR

This paper uses mean-field theory to study the contact variable in the BCS-BEC crossover of ultracold Fermi gases with finite-range interactions, revealing a potential quantum transition at large interaction ranges.

Contribution

It introduces a finite-range potential model to explore the entire BCS-BEC crossover without approximations, validating mean-field theory and predicting a quantum transition-like behavior.

Findings

Validation of mean-field theory across the crossover

Prediction of a quantum transition at large potential ranges

Analysis of the contact variable as a function of interaction parameters

Abstract

Using mean-field theory for the Bardeen-Cooper-Schriefer (BCS) to the Bose-Einstein condensate (BEC) crossover we investigate the ground state thermodynamic properties of an interacting homogeneous Fermi gas. The interatomic interactions modeled through a finite range potential allows us to explore the entire region from weak to strong interacting regimes with no approximations. To exhibit the thermodynamic behavior as a function of the potential parameters in the whole crossover region, we concentrate in studying the contact variable, the thermodynamic conjugate of the inverse of the s-wave scattering length. Our analysis allows us to validate the mean-field approach across the whole crossover. It also leads to predict a quantum transition-like in the case when the potential range becomes large. This finding is a direct consequence of the k-dependent energy gap for finite interaction range potentials.