BEC-BCS Crossover in the Epsilon Expansion

TL;DR

This paper extends the epsilon expansion method to finite scattering lengths to analyze the BEC-BCS crossover in cold Fermi gases, providing analytical expressions for the chemical potential ratio across different regimes.

Contribution

The study develops a resummation technique and extends the epsilon expansion to finite scattering lengths, enabling analysis of the BEC-BCS crossover.

Findings

Calculated mu/eF as a function of eta across regimes

Found good agreement with Quantum Monte Carlo results

Derived analytical formulas near unitarity, BEC, and BCS limits

Abstract

The epsilon expansion (expansion around four spacial dimensions) developed by Nishida and Son for a cold fermi gas with infinite scattering length is extended to finite scattering length to study the BEC-BCS crossover. A resummation of higher order logarithms and a suitable extension of fermion coupling in d-dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, mu/eF, is computed to next-to-leading order in the epsilon expansion as a function of eta=1/(a kF), where a is the scattering length and kF is the Fermi momentum in a non-interacting system. Near the unitarity limit eta->0, we found mu/eF=0.475-0.707 eta-0.5 eta^2. Near the BEC limit eta->infinity, mu/eF=0.062/eta - eta^2, while near the BCS limit eta->-infinity, mu/eF=1+0.707/eta. Overall good agreement with Quantum Monte Carlo results is found.