Resonance effects on the crossover of bosonic to fermionic superfluidity

TL;DR

This paper develops a theoretical framework to understand how resonance effects influence the crossover from bosonic to fermionic superfluidity in atomic gases, especially considering narrow Feshbach resonances and energy-dependent scattering.

Contribution

It introduces a model that incorporates energy dependence of the scattering phase shift, extending beyond the broad resonance approximation to include narrow resonances.

Findings

Energy dependence of scattering significantly affects superfluid properties.

BCS-like nonlocal solutions can emerge under resonance scattering conditions.

The framework can be calibrated with realistic atomic scattering data.

Abstract

Feshbach scattering resonances are being utilized in atomic gases to explore the entire crossover region from a Bose-Einstein Condensation (BEC) of composite bosons to a Bardeen-Cooper-Schrieffer (BCS) of Cooper pairs. Several theoretical descriptions of the crossover have been developed based on an assumption that the fermionic interactions are dependent only on the value of a single microscopic parameter, the scattering length for the interaction of fermion particles. Such a picture is not universal, however, and is only applicable to describe a system with an energetically broad Feshbach resonance. In the more general case in which narrow Feshbach resonances are included in the discussion, one must consider how the energy dependence of the scattering phase shift affects the physical properties of the system. We develop a theoretical framework which allows for a tuning of the scattering phase shift and its energy dependence, whose parameters can be fixed from realistic scattering solutions of the atomic physics. We show that BCS-like nonlocal solutions may build up in conditions of resonance scattering, depending on the effective range of the interactions.