Variational Study of $\lambda$- and $N$-Atomic Configurations Interacting with an Electromagnetic Field of $2$ Modes

TL;DR

This paper investigates the quantum phase diagrams of $mbda$- and $N$-atomic configurations interacting with two electromagnetic modes, revealing normal and super-radiant regimes with detailed subregion structures.

Contribution

It introduces a variational method to analyze the phase diagrams of atomic configurations interacting with two modes, aligning well with exact quantum solutions and detailing observable properties.

Findings

Identification of normal and super-radiant regimes.

Subdivision of super-radiant phases into multiple subregions.

Good agreement between variational and exact quantum results.

Abstract

A study of the $\lambda$- and $N$-atomic configurations under dipolar interaction with $2$ modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both configurations exhibit normal and collective (super-radiant) regimes. While the latter in the $\lambda$-configuration divides itself into $2$ subregions, corresponding to each of the modes, that in the $N$-configuration may be divided into $2$ or $3$ subregions depending on whether the field modes divide the atomic system into $2$ separate subsystems or not. Our variational procedure compares well with the exact quantum solution. The properties of the relevant field and matter observables are obtained.