Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split

TL;DR

This paper investigates the ground state properties of a few-boson system in a one-dimensional hard wall potential with a split, analyzing correlation, density, and momentum distributions across different interaction strengths and barrier heights.

Contribution

It provides an exact analysis of the ground state using Bose-Fermi mapping in the Tonks-Girardeau limit and employs exact diagonalization for finite interactions, revealing interference effects.

Findings

Secondary peaks in momentum distribution indicate particle interference.

Interference effects are stronger with larger barrier and weaker interactions.

Exact wavefunctions are constructed for different interaction regimes.

Abstract

We carry out a detailed examination of the ground state property of few-boson system in a one-dimensional hard wall potential with a $\delta -$ split in the center. In the Tonks-Girardeau limit with infinite repulsion between particles, we use the Bose-Fermi mapping to construct the exact $N-$ particle ground state wavefunction which allows us to study the correlation properties accurately. For the general case with finite inter-particle interaction, the exact diagonalization method is exploited to study the ground-state density distribution, occupation number distribution, and momentum distribution for variable interaction strengths and barrier heights. The secondary peaks in the momentum distribution reveal the interference between particles on the two sides of the split, which is more prominent for large barrier strength and small interaction strength.