Tonks-Girardeau gas, super-Tonks-Girardeau gas, and bound states of one-dimensional bosons in a hard-wall trap

TL;DR

This paper analyzes one-dimensional bosonic gases in a hard-wall trap, revealing phase transitions and properties of Tonks-Girardeau, super-Tonks-Girardeau, and bound states using Bethe Ansatz solutions.

Contribution

It provides a detailed characterization of quantum phases and phase transitions of 1D bosonic gases in a hard-wall trap, including the identification of matching points in the phase diagram.

Findings

TG and STG gases have identical profiles at strong interaction

TG and bound states connect smoothly at weak interaction

Energy spectrum and correlation functions elucidate phase behavior

Abstract

We investigate the Bose gas with repulsive or attractive interactions between atoms in the scheme of Bethe Ansatz equation in a hard wall trap. Three typical quantum phases in the current research of 1D interacting cold atoms are clarified in terms of the energy spectrum, single particle density distribution and two-particle correlation function. We identify two matching points in the phase diagram, i.e. the TG and STG gas show the same profiles at the strongly interacting point $-1/\gamma=0$, and in the weakly interacting limit $\gamma=0$ the ground states TG and BS join to each other smoothly.