Energy spectrum of harmonically trapped two-component Fermi gases: Three- and Four-Particle Problem

TL;DR

This paper numerically analyzes the energy spectrum of small two-component Fermi gases across the BCS-BEC crossover, revealing insights into strongly-interacting regimes using stochastic variational and hyperspherical coordinate methods.

Contribution

It provides the first detailed numerical energy spectra for four-fermion systems across the BCS-BEC crossover, including angular momentum and parity considerations.

Findings

Energy spectra vary smoothly with scattering length.

Hyperspherical coordinates facilitate quantum number assignment.

Insights into the unitary regime are obtained.

Abstract

Trapped two-component Fermi gases allow for the investigation of the so-called BCS-BEC crossover by tuning the interspecies atom-atom $s$-wave scattering length scattering $a^{(aa)}$ from attractive to repulsive, including vanishing and infinitely large values. Here, we numerically determine the energy spectrum of the equal-mass spin-balanced four-fermion system---the smallest few-particle system that exhibits BCS-BEC crossover-like behavior---as a function of $a^{(aa)}$ using the stochastic variational approach. For comparative purposes, we also treat the two- and three-particle systems. States with vanishing and finite total angular momentum as well as with natural and unnatural parity are considered. In addition, the energy spectrum of weakly-attractive and weakly-repulsive gases is characterized by employing a perturbative framework that utilizes hyperspherical coordinates. The hyperspherical coordinate approach allows for the straightforward assignment of quantum numbers and furthermore provides great insights into the strongly-interacting unitary regime.