Effective-range dependence of two-dimensional Fermi gases

TL;DR

This paper introduces a pseudopotential model to study how the effective interaction range influences the properties of two-dimensional Fermi gases across the BEC-BCS crossover, using mean-field and Monte Carlo methods.

Contribution

It develops a new pseudopotential for effective ranges and applies it to analyze ground-state properties of 2D Fermi gases across different interaction regimes.

Findings

Ground-state energy varies with effective range.

Contact and condensate fraction depend on interaction parameters.

Momentum distribution and pair correlations are characterized across the crossover.

Abstract

The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges $-1.5 \leq k_\mathrm{F}^2 R_\mathrm{eff}^2 \leq 0$, here $R_\mathrm{eff}$ is the effective range and $k_\mathrm{F}$ is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit $k_\mathrm{F}^2 R_\mathrm{eff}^2 \to -\infty$ is a gas of bosons with zero binding energy, whereas $\ln(k_\mathrm{F} a) \to -\infty$ corresponds to noninteracting bosons with infinite binding energy.