Correlation properties of a three-body bosonic mixture in a harmonic trap

TL;DR

This paper introduces a pair correlated wave function approach to analyze the ground-state properties of a three-body bosonic mixture in a harmonic trap, accurately capturing various interaction regimes and enabling study of complex mixed interactions.

Contribution

The study presents a simple yet effective wave function method that reproduces known analytical results and extends to mixed interaction cases in three-body bosonic systems.

Findings

Accurately reproduces zero and infinite repulsion cases

Agrees with exact diagonalization across interaction regimes

Provides insights into mixed interaction probability densities

Abstract

We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For equal interactions this approach is able to reproduce the known analytical cases of zero and infinite repulsion. We show that our results for the correlations agree with the exact diagonalization in all interaction regimes and with analytical results for the strongly repulsive impurity. This method also enables us to access the more complicated cases of mixed interactions, and the probability densities of these systems are analyzed.