Boson Pairs in a One-dimensional Split Trap

TL;DR

This paper investigates the properties of a pair of ultracold bosonic atoms in a one-dimensional trap with a tunable barrier, analyzing their ground state, entanglement, and effects of interactions, with analytical and numerical methods.

Contribution

It provides a comprehensive analysis of boson pairs in a split trap, including analytical solutions in the Tonks-Girardeau limit and numerical results for finite interactions.

Findings

Analytical expressions for the ground state in the Tonks-Girardeau limit.

Numerical characterization of the ground state for finite interactions.

Insights into pair interactions in double-well potentials.

Abstract

We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap centre. The full characterisation of the ground state is done by calculating the reduced single-particle density, the momentum distribution and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.