SU(N) Fermions in a One-Dimensional Harmonic Trap

Abstract

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a new numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz - derived for a Heisenberg SU(2) spin chain - is extendable to these N-component systems. Lastly, we consider balanced SU(N) Fermi gases that have an equal number of particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N-component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.

15 pages, 6 figures

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Cited by in corpus (21)

• One-dimensional mixtures of several ultracold atoms: a review
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Evidence for Bosonization in a three-dimensional gas of SU($N$) fermions
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Realizing time crystals in discrete quantum few-body systems
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• Dynamics of spin and density fluctuations in strongly interacting few-body systems
• Impenetrable SU(N) fermions in one-dimensional lattices
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• Systematic interpolatory ansatz for one-dimensional polaron systems
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• On the direct diagonalization method for a few particles trapped in harmonic potentials
• Impurity immersed in a two-component few-fermion mixture in a one-dimensional harmonic trap