Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides

TL;DR

This paper uses a generalized Fermi-Bose mapping to find exact ground states of strongly interacting ultracold gas mixtures in tight waveguides, extending known models and analyzing their properties.

Contribution

It introduces a generalized mapping method to exactly solve models of mixed ultracold gases with strong interactions in 1D.

Findings

Exact density profiles in harmonic traps

Single-particle density matrices and momentum distributions

Analysis of ground state degeneracy and splitting

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.