Degeneracies in trapped two-component Fermi gases

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.

5 pages with 4 figures + 5 pages of supplemental material

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Cited by in corpus (8)

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• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas
• Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations
• Entanglement production by statistical operators
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: spin-independent interactions and spin-dependent external fields
• Long-lived states with well-defined spins in spin-$1/2$ homogeneous Bose gases
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: II. Spin-dependent two-body interactions