Two electrons in harmonic confinement coupled to light in a cavity

TL;DR

This paper presents an exact method to calculate the energy and wave functions of a two-electron system in harmonic confinement coupled to light, applicable for any coupling strength, by separating and solving relative and center of mass motions.

Contribution

It introduces a diagonalization approach that exactly solves the coupled light-matter system without approximations, focusing on the center of mass motion.

Findings

Wave functions of light-matter hybrid states are computed.

The method is valid for any light-matter coupling strength.

Analytical solutions for the relative motion are utilized.

Abstract

The energy and wave function of a harmonically confined two-electron system coupled to light is calculated by separating the wave functions of the relative and center of mass (CM) motions. The relative motion wave function has a known quasi-analytical solution. The light only couples to the CM variable and the coupled equation can be solved with diagonalization without approximations. The approach works for any coupling strength. Examples of wave functions of light-matter hybrid states are presented.