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

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 $1/r$.

31 pages, 11 figures, In this version, several mistakes and typos have been corrected. The Appendix C for the dilute BEC limit and the molecule-molecule repulsion has been added. The discussion about the nuclear contact has been updated

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Cited by in corpus (7)

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• Brueckner $G$-matrix approach to two-dimensional Fermi gases with the finite-range attractive interaction
• Nonuniversal Equation of State of a Quasi-2D Bose Gas in Dimensional Crossover
• Quartet correlations near the surface of $N=Z$ nuclei
• Finite-range effect in the two-dimensional density-induced BCS-BEC crossover
• Quarkyonic matter and hadron-quark crossover from an ultracold atom perspective
• Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids