Degeneracies in trapped two-component Fermi gases

TL;DR

This paper uncovers new inter-system degeneracies in two-component Fermi gases with equal masses under harmonic confinement, revealing symmetries that connect different particle number configurations across all scattering lengths.

Contribution

It identifies and explains previously unobserved degeneracies between different Fermi gas systems using group theory, expanding understanding of their spectral symmetries.

Findings

Degeneracies occur between (n1+1,n2-1) and (n1,n2) systems for all scattering lengths.

Explicit demonstration for systems with total particles 4, 5, and 6.

Symmetries explained through a group theoretical framework.

Abstract

We report on previously unobserved inter-system degeneracies in two-component equal-mass Fermi gases with interspecies zero-range interactions under isotropic harmonic confinement. Over the past 10 years, two-component Fermi gases consisting of $n_1$ spin-up and $n_2$ spin-down atoms with interspecies zero-range interactions have become a paradigm for modeling condensed matter systems, nuclear matter and neutron matter. We show that the eigen energies of the $(n_1+1,n_2-1)$ system are degenerate with the eigen energies of the $(n_1,n_2)$ system for any s-wave scattering length $a_s$, including infinitely large, positive and negative $a_s$. The existence of the inter-system degeneracies is demonstrated explicitly for few-body systems with $n_1+n_2=4, 5$ and 6. The degeneracies and associated symmetries are explained within a group theoretical framework.