BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses

TL;DR

This paper investigates the energy spectrum of a two-component Fermi gas with unequal masses across the BEC-BCS crossover in a trap, using exact and Monte Carlo methods, and explores universal properties and effective interactions.

Contribution

It introduces a combined approach using basis set expansion and diffusion Monte Carlo to analyze the energy spectrum of mass-imbalanced Fermi gases across the BEC-BCS crossover.

Findings

Energy spectra agree with analytical corrections on BEC and BCS sides.

Extracted scattering length and effective range up to mass ratio 20.

Universal parameter  determined for various mass ratios.

Abstract

We determine the energetically lowest lying states in the BEC-BCS crossover regime of s-wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schrodinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with N=4 fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to N=20 fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the s-wave scattering length a_s for N=2-20 fermions and different mass ratios \kappa of the two species. On the BEC and BCS sides, our energies agree with analytically-determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to \kappa = 20. Our energies for the strongly-interacting trapped system in the unitarity regime show no shell structure, and are well described by a simple expression, whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter \xi for the trapped system for various \kappa is determined, and comparisons with results for the homogeneous system are presented.