Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study

TL;DR

This study uses exact diagonalization to analyze the transition of spinless bosons in a 1D trap from Bose-Einstein condensate to Tonks-Girardeau gas, revealing detailed properties across interaction regimes.

Contribution

It provides a comprehensive, quantitative analysis of the ground state properties of 1D bosons across the entire interaction spectrum using exact diagonalization.

Findings

Identifies the transition point between mean-field and Tonks-Girardeau regimes.

Characterizes the momentum distribution change during the transition.

Quantifies interaction strengths delimiting different regimes.

Abstract

We study ground state properties of spinless, quasi one-dimensional bosons which are confined in a harmonic trap and interact via repulsive delta-potentials. We use the exact diagonalization method to analyze the pair correlation function, as well as the density, the momentum distribution, different contributions to the energy and the population of single-particle orbitals in the whole interaction regime. In particular, we are able to trace the fascinating transition from bosonic to fermi-like behavior in characteristic features of the momentum distribution which is accessible to experiments. Our calculations yield quantitative measures for the interaction strength limiting the mean-field regime on one side and the Tonks-Girardeau regime on the other side of an intermediate regime.