# Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

## TL;DR

This paper introduces an exactly solvable model for two Rydberg-dressed atoms in a 2D harmonic trap, analyzing their eigenstates, correlations, and potential for generalization to higher dimensions.

## Contribution

It provides a novel exactly solvable model for Rydberg-dressed atoms in two dimensions, including classification of eigenstates and a method to extend solutions to higher dimensions.

## Key findings

- Eigenstates classified by excitations and angular momentum
- Inter-particle correlations depend on interaction parameters
- Solutions can be generalized to higher dimensions

## Abstract

Exactly solvable model of two Rydberg-dressed atoms moving in a quasi-two-dimensional harmonic trap is introduced and its properties are investigated. Depending on the strength of inter-particle interactions and the critical range of the potential, the two-particle eigenstates are classified with respect to the excitations of the center-of-mass motion, relative angular momentum, and relative distance variable. Having these solutions in hand, we discuss inter-particle correlations as functions of interaction parameters. We also present a straightforward prescription of how to generalize obtained solutions to higher dimensions.