Compact cavity-dressed Hamiltonian framework at arbitrarily strong light-matter coupling

TL;DR

This paper introduces a non-perturbative, compact Hamiltonian framework for strongly coupled light-matter systems that improves accuracy and efficiency over traditional methods, applicable to multimode and leaky cavities.

Contribution

It develops a cavity-dressed Hamiltonian mapping technique that yields convergent, closed-form models for hybrid systems in the ultrastrong coupling regime, surpassing conventional approaches.

Findings

Accurate spectral predictions for the quantum Rabi model.

Converging ground-state and thermal observables.

Efficient phase diagram determination for the Dicke-Heisenberg lattice.

Abstract

We present a non-perturbative Hamiltonian mapping method for quantum systems strongly coupled to a quantized field mode (cavity), yielding compact closed-form representations of hybrid light-matter systems. The mapping method builds on an entangling transformation of photonic and atomic degrees of freedom. By truncating the resulting cavity-dressed Hamiltonian (CDH) to successively larger excitation sectors, we construct a series of compact models that converge to the exact limit, outpacing conventional approaches even in the challenging resonant and ultrastrong light-matter regime. The mapping principle also applies to multimode cavities coupled to matter through noncommuting operators and to leaky cavities. We benchmark the CDH framework on the quantum Rabi model, demonstrating accurate spectral predictions in both weak and strong coupling regimes, together with converging ground-state and thermal observables. We study the Dicke-Heisenberg lattice model and determine its phase diagram under resonant and strong light-matter coupling, achieving significant computational savings over brute-force simulations and identifying cavity-mediated spin correlations both analytically and numerically. The closed-form and compactness of the CDH provide both physical insight and enhanced computational efficiency, facilitating studies of strongly coupled hybrid light-matter systems.