Ground-state properties of interacting two-component Bose gases in a hard-wall trap

TL;DR

This paper studies the ground-state properties of two-component Bose gases in a hard-wall trap, revealing how their density distributions evolve with interaction strength using Bethe ansatz and numerical methods.

Contribution

It provides an exact analytical solution for the ground state in the equal interaction case and characterizes the distribution crossover in strongly interacting regimes.

Findings

Density distribution transitions from Gaussian to Fermi-like with increasing repulsion.

Component distributions are proportional to total density, consistent with experiments.

Strong interspecies interactions lead to composite fermionization with N peaks.

Abstract

We investigate ground-state properties of interacting two-component Bose gases in a hard-wall trap using both the Bethe ansatz and exact numerical diagonalization method. For equal intra- and inter-atomic interaction, the system is exactly solvable. Thus the exact ground state wavefunction and density distributions for the whole interacting regime can be obtained from the Bethe ansatz solutions. Since the ground state is a degenerate state with total spin S=N/2, the total density distribution are same for each degenerate state. The total density distribution evolves from a Gauss-like Bose distribution to a Fermi-like one as the repulsive interaction increases. The distribution of each component is N_i/N of the total density distribution. This is approximately true even in the experimental situation. In addition the numerical results show that with the increase of interspecies interaction the distributions of two Tonks-Girardeau gases exhibit composite fermionization crossover with each component developing N peaks in the strongly interacting regime.