Small two-component Fermi gases in a cubic box with periodic boundary conditions

TL;DR

This study investigates the eigen energies of small two-component Fermi gases in a cubic box with periodic boundary conditions, focusing on universal properties and energy spectra across different interaction regimes.

Contribution

The paper introduces a correlated Gaussian basis set approach to accurately compute eigen energies and analyze universal behavior in small Fermi gases with varying scattering lengths.

Findings

Eigen energies extrapolated to zero-range limit for up to four particles

Excellent agreement between perturbation theory and numerical results in BCS regime

Comparison with existing literature for infinite scattering length case

Abstract

The properties of two-component Fermi gases become universal if the interspecies s-wave scattering length $a_s$ and the average interparticle spacing are much larger than the range of the underlying two-body potential. Using an explicitly correlated Gaussian basis set expansion approach, we determine the eigen energies of two-component Fermi gases in a cubic box with periodic boundary conditions as functions of the interspecies s-wave scattering length and the effective range of the two-body potential. The universal properties of systems consisting of up to four particles are determined by extrapolating the finite-range energies to the zero-range limit. We determine the eigen energies of states with vanishing and finite momentum. In the weakly-attractive BCS regime, we analyze the energy spectra and degeneracies using first-order degenerate perturbation theory. Excellent agreement between the perturbative energy shifts and the numerically determined energies is obtained. For the infinitely large scattering length case, we compare our results - where available - with those presented in the literature.