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arXiv · 2512.05196

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

Davis M. Welakuh·Vasil Rokaj·Michael Ruggenthaler·Angel Rubio
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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.

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Davis M. Welakuh, Vasil Rokaj, Michael Ruggenthaler, Angel Rubio. 2025-12-04. Multimode equilibrium approximations in light-matter systems from weak to strong coupling. https://arxiv.org/abs/2512.05196

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