Effective theory for matter in non-perturbative cavity QED

TL;DR

This paper develops a non-perturbative effective theory for matter coupled to complex cavity systems, capturing cavity-induced interactions and applicable to various bosonic bath systems beyond cavity QED.

Contribution

It introduces a novel, non-perturbative path integral approach that accounts for image charges, the $A^2$ term, and arbitrary cavity geometries, providing a versatile framework.

Findings

Effective Hamiltonian with explicit cavity-induced interactions

Numerical analysis of finite-size scaling in the Dicke model

Application to photon condensation, electron gases, and magnetic interactions

Abstract

Starting from a general material system of $N$ particles coupled to a cavity, we use a coherent-state path integral formulation to produce a non-perturbative effective theory for the material degrees of freedom. We tackle the effects of image charges, the $A^2$ term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-$N$ limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature.