Interaction-Range Effects and Universality in the BCS-BEC Crossover of Spin-Orbit Coupled Fermi Gases

TL;DR

This paper investigates how finite interaction range and spin-orbit coupling influence the BCS-BEC crossover in ultracold Fermi gases, revealing universal behavior in certain regimes and implications for topological states.

Contribution

It demonstrates the interplay between interaction range and spin-orbit coupling in the crossover, highlighting conditions for universality and topological transitions in ultracold fermionic gases.

Findings

Universal behavior persists below the topological transition threshold when using pair correlation length.

The topological transition threshold is influenced by interactions mainly in the BEC-like regime.

Universality breaks down in large pair size regimes above the threshold.

Abstract

We explore the evolution of a ultracold quantum gas of interacting fermions crossing from a Bardeen-Cooper-Schrieffer (BCS) superfluidity to a Bose-Einstein condensation (BEC) of molecular bosons in the presence of a tunable-range interaction among the fermions and of an artificial magnetic field, which can be used to simulate a pseudo-spin-orbit coupling (SOC) and to produce topological states. We find that the crossover is affected by a competition between the finite range of the interaction and the SOC and that the threshold $\lambda_B$ for the topological transition is affected by the interactions only in the small pair size, BEC-like, regime. Below $\lambda_B$, we find persistence of universal behavior in the critical temperature, chemical potential, and condensate fraction, provided that the pair correlation length is used as a driving parameter. Above threshold, universality is lost in the regime of large pair sizes. Here, the limiting ground state departs from a weakly-interacting BCS-like, so that a different description is required. Our results can be relevant in view of current experiments with cold atoms in optical cavities, where tunable-range effective atomic interactions can be engineered.