Casimir interaction among heavy fermions in the BCS-BEC crossover

TL;DR

This paper explores the Casimir interaction among heavy fermions in a two-species Fermi gas across the BCS-BEC crossover, revealing p-wave attraction behavior and effects of dimensional confinement.

Contribution

It introduces a theoretical analysis of heavy fermion interactions using the Born-Oppenheimer approximation across different interaction regimes and dimensions.

Findings

P-wave attraction peaks between BCS and unitarity limits.

P-wave interaction is stronger in two dimensions.

Effective interaction aligns with perturbative results in the BCS limit.

Abstract

We investigate a two-species Fermi gas with a large mass ratio interacting by an interspecies short-range interaction. Using the Born-Oppenheimer approximation, we determine the interaction energy of two heavy fermions immersed in the Fermi sea of light fermions as a function of the s-wave scattering length. In the BCS limit, we recover the perturbative calculation of the effective interaction between heavy fermions. The p-wave projection of the effective interaction is attractive in the BCS limit while it turns out to be repulsive near the unitarity limit. We find that the p-wave attraction reaches its maximum between the BCS and unitarity limits, where the maximal p-wave pairing of heavy minority fermions is expected. We also investigate the case where the heavy fermions are confined in two dimensions and the p-wave attraction between them is found to be stronger than that in three dimensions.