Density-functional theory of two-component Bose gases in one-dimensional harmonic traps

TL;DR

This paper uses density-functional theory with Bethe-ansatz-based local-density approximation to analyze the ground-state properties of two-component Bose gases in one-dimensional harmonic traps, revealing a crossover from Bose to Fermi-like distributions as interactions increase.

Contribution

It introduces a Bethe-ansatz-based local-density approximation for density-functional calculations of two-component Bose gases, including a mapping to the Yang-Gaudin model for exact solutions.

Findings

Density distributions evolve from Bose to Fermi-like with increasing interaction.

Binary mixture can be mapped to a two-component Fermi gas via Bose-Fermi transformation.

System exhibits composite-fermionization crossover as inter-species interaction increases.

Abstract

We investigate the ground-state properties of two-component Bose gases confined in one-dimensional harmonic traps in the scheme of density-functional theory. The density-functional calculations employ a Bethe-ansatz-based local-density approximation for the correlation energy, which accounts for the correlation effect properly in the full physical regime. For the binary Bose mixture with spin-independent interaction, the homogeneous reference system is exactly solvable by the Bethe-ansatz method. Within the local-density approximation, we determine the density distribution of each component and study its evolution from Bose distributions to Fermi-like distribution with the increase in interaction. For the binary mixture of Tonks-Girardeau gases with a tunable inter-species repulsion, with a generalized Bose-Fermi transformation we show that the Bose mixture can be mapped into a two-component Fermi gas, which corresponds to exact soluble Yang-Gaudin model for the homogeneous system. Based on the ground-state energy function of the Yang-Gaudin model, the ground-state density distributions are calculated for various inter-species interactions. It is shown that with the increase in inter-species interaction, the system exhibits composite-fermionization crossover.