Multimode equilibrium approximations in light-matter systems from weak to strong coupling

TL;DR

This paper develops and compares approximation methods for modeling equilibrium properties of light-matter systems in complex multi-mode photonic environments, effective across weak to strong coupling regimes.

Contribution

It introduces new approximation techniques that simplify multi-mode photonic environments, enabling accurate equilibrium analysis in complex quantum light-matter systems.

Findings

Effective polarization-only approach captures key equilibrium effects.

Few effective modes suffice for accurate modeling.

Methods applicable to atomic, molecular, and condensed matter systems.

Abstract

In this work, we detail different approaches to treat multi-mode photonic environments within non-relativistic quantum electrodynamics in the long-wavelength approximation efficiently. Specifically we show that for equilibrium properties of coupled light-matter systems, we can approximately capture the effects of multi-mode photonic environments on matter systems by either only keeping the polarization part of the electric field in the length-gauge formulation or by a few effective modes. We present a comprehensive set of approximation methods designed to accurately capture equilibrium phenomena in quantum light-matter systems across a range of complex photonic environments, from weak to strong coupling. These methods are applied to atomic and molecular models as well as to a two-dimensional quantum ring, demonstrating the versatility of our approach and laying the groundwork for first-principles simulations of real materials in cavity quantum electrodynamics.