Effective Equilibrium Theory of Quantum Light-Matter Interaction in Cavities: Extended Systems and the Long Wavelength Approximation

TL;DR

This paper develops a non-perturbative, effective theory for quantum light-matter interactions in cavities, accounting for realistic cavity parameters and extending to bulk systems, advancing the understanding of cavity materials engineering.

Contribution

It introduces a realistic, Hamiltonian-based framework for cavity light-matter interactions that includes multimode, dispersive effects and finite mirror reflectivity, applicable to extended systems.

Findings

Effective single-mode description with finite mode volume for extended systems

Inclusion of cavity mirror reflectivity avoids double counting of light-matter coupling

Framework applicable to low-dimensional crystals in realistic cavities

Abstract

When light and matter interact strongly, the resulting hybrid system inherits properties from both constituents, allowing one to modify material behavior by engineering the surrounding electromagnetic environment. This concept underlies the emerging paradigm of cavity materials engineering, which aims at the control of material properties via tailored vacuum fluctuations of dark photonic environments. The theoretical description of such systems is challenging due to the combined complexity of extended electronic states and quantum electromagnetic fields. Here, we derive an effective, non-perturbative theory for low-dimensional crystals embedded in a Fabry-P\'erot resonator, within the long-wavelength limit. Our approach incorporates the multimode and dispersive nature of the cavity field and reduces it to an effective single-mode description by imposing the condition of negligible momentum transfer from light to matter. Importantly, the resulting effective mode is characterized by a finite mode volume-even in the limit of extended cavities-which is directly linked to realistic cavity parameters. This ensures that the light-matter coupling remains finite in bulk systems. By explicitly accounting for the finite reflectivity of cavity mirrors, our theory also avoids double counting the contribution from free-space light-matter coupling. Overall, our results provide a robust and realistic framework for describing cavity-matter interactions at the Hamiltonian level, incorporating the electromagnetic environment beyond the idealized perfect-mirror approximation.