Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap

TL;DR

This paper analyzes the ground state properties of one-dimensional ultracold Bose gases in a hard-wall trap, revealing how their density and correlation functions evolve across different interaction regimes using Bethe ansatz solutions.

Contribution

It derives explicit ground state wave functions and solves Bethe ansatz equations across the full interaction spectrum, including the Tonks and strongly attractive limits.

Findings

Density profiles exhibit Fermi-like behavior in the Tonks limit.

Bosons form a bound state in the strongly attractive limit.

Density and correlation functions show continuous crossover behavior.

Abstract

We investigate the ground state of the system of N bosons enclosed in a hard-wall trap interacting via a repulsive or attractive $\delta$-function potential. Based on the Bethe ansatz method, the explicit ground state wave function is derived and the corresponding Bethe ansatz equations are solved numerically for the full physical regime from the Tonks limit to the strongly attractive limit. It is shown that the solution takes different form in different regime. We also evaluate the one body density matrix and second-order correlation function of the ground state for finite systems. In the Tonks limit the density profiles display the Fermi-like behavior, while in the strongly attractive limit the Bosons form a bound state of N atoms corresponding to the N-string solution. The density profiles show the continuous crossover behavior in the entire regime. Further the correlation function indicates that the Bose atoms bunch closer as the interaction constant decreases.