A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

TL;DR

This study investigates the superfluid properties of a unitary Fermi gas interacting via a finite-ranged potential, deriving key quantities like the pairing gap and chemical potential, and comparing results with mean-field and quantum Monte Carlo methods.

Contribution

The paper introduces a detailed model of a unitary Fermi gas using a finite-ranged potential and derives exact scattering solutions to analyze superfluid properties.

Findings

The pairing gap at the Fermi energy closely matches mean-field contact potential results.

The average gap in the zero-range and unitary limits is approximately 0.42 E_F.

The chemical potential in the zero-range limit aligns with contact potential calculations.

Abstract

We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution of the potential, we derive two-body ${\mathbf T}$-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitary regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated in mean-field theory with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be $0.42 E_F$ which is quite close to the recent result of the quantum Monte Carlo simulation [2018 {\rm Phys. Rev.A} {\bf 97}, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.