Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides

Abstract

A generalized Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.

Revised to discuss splitting of degenerate ground manifold for large but finite BB and BF repulsions; accepted by PRL

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• Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap
• Excitations of attractive 1-D bosons: Binding vs. fermionization
• Ground-state properties of interacting two-component Bose gases in a hard-wall trap
• Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons
• Binding between two-component bosons in one dimension
• Transport, atom blockade and output coupling in a Tonks-Girardeau gas
• Hard-core Bose-Fermi mixture in one-dimensional split traps
• Mixture of Tonks-Girardeau gas and Fermi gas in one-dimensional optical lattices