Polariton spectrum of the Dicke-Ising model

TL;DR

This paper diagonalizes the Dicke-Ising model to analyze how dipole-dipole and light-matter interactions influence the ground state and excitation spectrum in cavity QED systems.

Contribution

It introduces a general method using higher order Holstein-Primakoff transformation to solve the normal phase for large dipole-dipole interactions.

Findings

Interplay between dipole-dipole and light-matter coupling affects virtual excitations.

Method enables analysis of the model up to the ferromagnetic phase transition.

Results clarify the ground-state properties in strongly interacting regimes.

Abstract

The Dicke-Ising model describes cavity quantum electrodynamics setups in which dipoles couple not only with the photonic cavity field but also to each other through dipole-dipole interaction. In this work we diagonalise such a model in terms of bosonic polaritonic operators for arbitrarily large values of the light-matter coupling and for values of the dipole-dipole interaction until the onset of the ferromagnetic Ising phase transition. In order to accomplish this task we exploit higher order terms of the Holstein-Primakoff transformation, developing a general method which allows to solve the normal phase of the Ising model in term of bosonic excitations for large values of the dipole-dipole interaction. Our results shed light on the interplay between the dipole-dipole and the light-matter coupling strengths, and their effect on the virtual excitations which populate the ground-state when the interactions become comparable with the bare transition frequency.