Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics

TLDR

Experiments at the interface of quantum optics and chemistry have shown that strong light–matter coupling can significantly alter molecular and solid‑state properties, yet nonrelativistic QED treatments frequently omit the quadratic coupling terms that are theoretically present. The study aims to clarify the physical origin and substantial impact of the diamagnetic and self‑polarization terms, showing why neglecting them leads to unphysical results. The authors analyze these quadratic terms within the nonrelativistic QED framework, demonstrating their effects on gauge invariance, basis‑set dependence, and system stability. They show that omitting the quadratic terms causes loss of gauge invariance, basis‑set dependence, disintegration of bound states in the basis‑set limit, unphysical ground‑state radiation, and artificial dependence on the static dipole, and identify conditions where these effects could be observed.

Abstract

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light–matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light–matter systems, the presented results also indicate conditions under which those effects might become accessible.