Simulation of an inhomogeneous Fermi gas through the BCS-BEC crossover

TL;DR

This paper uses variational quantum Monte Carlo simulations to study the BCS-BEC crossover in an inhomogeneous Fermi gas at zero temperature, analyzing ground state properties across different interaction regimes.

Contribution

It introduces a variational wave function approach for large particle numbers to accurately model the BCS-BEC transition in an inhomogeneous Fermi gas.

Findings

Virial relation approximately valid in the crossover regime

Ground state properties depend on the s-wave scattering length

Two-body correlations influenced by trap and interaction potential

Abstract

We perform a variational quantum Monte Carlo simulation of the transition from a Bardeen-Cooper-Schrieffer superfluid (BCS) to a Bose-Einstein condensate (BEC) at zero temperature. The model Hamiltonian involves an attractive short range two body interaction and the atoms number $2N =330$ is chosen so that, in the non-interacting limit, the ground state function corresponds to a closed shell configuration. The system is then characterized by the s-wave scattering length $a$ of the two-particle collisions in the gas, which is varied from negative to positive values, and the Fermi wave number $k_F$. Based on an extensive analysis of the s-wave two-body problem, one parameter variational many-body wave functions are proposed to describe the ground state of the interacting Fermi gas from BCS to BEC states. We exploit properties of antisymmetrized many-body functions to develop efficient techniques that permit variational calculations for a large number of particles. It is shown that a virial relation between the energy per particle and the trapping energy is approximately valid for $-0.1<1/k_Fa<3.4$. The influence of the harmonic trap and the interaction potential as exhibited in two-body correlation functions is also analyzed.