Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths

TL;DR

This paper introduces a nonperturbative method for analyzing quantum light-matter systems across all coupling strengths, enabling effective modeling even at very strong interactions.

Contribution

It presents a unitary transformation approach that decouples light and matter in the strong coupling limit, facilitating systematic derivation of low-energy models.

Findings

Effective decoupling at strong coupling

Systematic derivation of low-energy Hamiltonians

Versatile application to various quantum models

Abstract

Quantum light-matter systems at strong coupling are notoriously challenging to analyze due to the need to include states with many excitations in every coupled mode. We propose a nonperturbative approach to analyze light-matter correlations at all interaction strengths. The key element of our approach is a unitary transformation that achieves asymptotic decoupling of light and matter degrees of freedom in the limit where light-matter interaction becomes the dominant energy scale. In the transformed frame, truncation of the matter/photon Hilbert space is increasingly well-justified at larger coupling, enabling one to systematically derive low-energy effective models, such as tight-binding Hamiltonians. We demonstrate the versatility of our approach by applying it to concrete models relevant to electrons in crystal potential and electric dipoles interacting with a cavity mode. A generalization to the case of spatially varying electromagnetic modes is also discussed.