Role of the effective range in the density-induced BEC-BCS crossover

TL;DR

This paper investigates how the effective range of interactions influences the BEC-BCS crossover in fermionic systems, revealing effects on superfluid properties, stability, and high-momentum behavior.

Contribution

It demonstrates the significance of the effective range in the density-induced BEC-BCS crossover, extending understanding beyond contact interactions.

Findings

Superfluid order parameter is suppressed at high densities.

Sound velocity shows non-monotonic behavior indicating stability.

High-momentum tail linked to contact parameter is observable when momentum is much less than 1/r.

Abstract

We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. Characterizing the non-local interaction in terms of the low-energy constants such as scattering length $a$ and effective range $r$, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a non-monotonic behavior reflecting mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum $k$ is much less than $1/r$.