BEC-BCS crossover of a trapped Fermi gas without using the local density approximation

TL;DR

This paper uses variational quantum Monte Carlo simulations to study the BEC-BCS crossover in a trapped Fermi gas, providing insights into the transition without relying on the local density approximation.

Contribution

It introduces a family of variational wave functions that capture the qualitative differences between BCS and BEC regimes in a trapped Fermi gas.

Findings

Calculated energies, densities, and correlation functions for different regimes.

Verified the virial relation and evaluated the β parameter at unitarity.

Compared results with those for homogeneous gases.

Abstract

We perform a variational quantum Monte Carlo simulation of an interacting Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based on the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlation functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are performed including the verification of the virial relation and the evaluation of the $\beta$ parameter.