Energetics and Structural Properties of Trapped Two-Component Fermi Gases

TL;DR

This paper investigates the energetics and structural properties of two-component Fermi gases in a harmonic trap using numerical methods, focusing on the BEC-BCS crossover, angular momentum, and excitation spectra, with insights from hyperspherical analysis.

Contribution

It introduces a combined use of Gaussian basis-set expansion and diffusion Monte Carlo methods to analyze small and large Fermi systems, providing new insights into their energetics and structure across different regimes.

Findings

Energy and structural properties vary with scattering length and mass ratio.

Odd-even oscillations in ground state energy relate to excitation gaps.

Hyperspherical analysis offers new understanding of angular momentum effects.

Abstract

Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range s-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd $N$, as functions of the s-wave scattering length and the mass ratio $\kappa$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum L=0 is calculated as a function of the mass ratio $\kappa$. The results are analyzed from a hyperspherical perspective, which offers new insights into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to N=30 atoms. We focus on the odd-even oscillations of the ground state energy of the equal-mass unitary system having up to N=30 particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.