Radial and Angular Correlations in a Confined System of Two Atoms in a Two-Dimensional Geometry

TL;DR

This paper investigates the ground-state correlations of two atoms confined in a two-dimensional harmonic trap, revealing how radial and angular correlations depend on interaction parameters and range, with implications for atomic system modeling.

Contribution

It provides a detailed analysis of radial and angular correlations in a 2D two-atom system with finite-range interactions, highlighting their independence and complex behaviors.

Findings

Radial and angular correlations are independent in the hardcore limit.

Correlations are significantly affected by the interaction range.

Radial correlations are generally weaker than angular correlations.

Abstract

We study the ground-state correlations between two atoms in a two-dimensional isotropic harmonic trap. We consider a finite-range soft-core interaction that can be applied to simulate various atomic systems. We provide detailed results on the dependence of the correlations on the parameters of the system. Our investigations show that in the hardcore limit, the wave function can be approximated as the product of the radial and angular components regardless of the interaction range. This implies that the radial and angular correlations are independent of one another. However, correlations within the radial and angular components persist and are heavily influenced by the interaction range. The radial correlations are generally weaker than the angular correlations. When soft-core interactions are considered, the correlations exhibit more complex behavior.