Mean-Field vs Monte-Carlo equation of state for the expansion of a Fermi superfluid in the BCS-BEC crossover

TL;DR

This paper compares Monte Carlo and mean-field equations of state for a Fermi superfluid in the BCS-BEC crossover, analyzing their predictions for expansion dynamics and agreement with experiments.

Contribution

It introduces a density functional approach based on these EOS to study superfluid expansion, highlighting differences in anisotropy reversal between regimes.

Findings

Both EOS models agree with experimental data for $^6$Li.

The released energy follows an accurate analytical formula in the BEC regime.

Faster anisotropy reversal occurs in the BCS regime for droplet expansion.

Abstract

The equation of state (EOS) of a Fermi superfluid is investigated in the BCS-BEC crossover at zero temperature. We discuss the EOS based on Monte-Carlo (MC) data and asymptotic expansions and the EOS derived from the extended BCS (EBCS) mean-field theory. Then we introduce a time-dependent density functional, based on the bulk EOS and Landau's superfluid hydrodynamics with a von Weizs\"acker-type correction, to study the free expansion of the Fermi superfluid. We calculate the aspect ratio and the released energy of the expanding Fermi cloud showing that MC EOS and EBCS EOS are both compatible with the available experimental data of $^6$Li atoms. We find that the released energy satisfies an approximate analytical formula that is quite accurate in the BEC regime. For an anisotropic droplet, our numerical simulations show an initially faster reversal of anisotropy in the BCS regime, later suppressed by the BEC fluid.