Abstract
We consider a mixture of one-dimensional strongly interacting Fermi gases with up to six components, subjected to a longitudinal harmonic confinement. In the limit of infinitely strong repulsions we provide an exact solution which generalizes the one for the two-component mixture. We show that an imbalanced mixture under harmonic confinement displays partial spatial separation among the components, with a structure which depends on the relative population of the various components. Furthermore, we provide a symmetry characterization of the ground and excited states of the mixture introducing and evaluating a suitable operator, namely the conjugacy class sum. We show that, even under external confinement, the gas has a definite symmetry which corresponds to the most symmetric one compatible with the imbalance among the components. This generalizes the predictions of the Lieb–Mattis theorem for a Fermionic mixture with more than two components.
Highlights
May 2016In the limit of infinitely strong repulsions we provide an exact solution which generalizes the one for the two-component mixture
Ultracold atomic gases made with rare-Earth elements cooled to quantum degeneracy and subjected to twodimensional optical lattices provide a beautiful realization of the model of one-dimensional multicomponent Fermi gases with strong and equal intercomponent repulsion among the species [1].In the absence of external harmonic confinement in the longitudinal direction, the system of multicomponent Fermions with intercomponent delta interactions is a generalization of the Yang–Gaudin Hamiltonian [2,3,4] and can be solved by nested Bethe Ansatz [5]
For each given mixture, we focus on the ground state and first manybody excited state with a symmetry different from the ground state one
Summary
In the limit of infinitely strong repulsions we provide an exact solution which generalizes the one for the two-component mixture. Even under external confinement, the gas has a definite symmetry which corresponds to the most symmetric one compatible with the imbalance among the components. This generalizes the predictions of the Lieb–Mattis theorem for a Fermionic mixture with more than two components
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