Degeneracies in Trapped Two-Component Fermi Gases

We report on previously unobserved intersystem 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 eigenenergies of the (n(1) + 1, n(2) - 1) system are degenerate with the eigenenergies 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 intersystem 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.