Reconciling quantum and classical spectral theories of ultrastrong coupling: Role of cavity bath coupling and gauge corrections

TL;DR

This paper demonstrates how to reconcile classical and quantum spectral theories in ultrastrong light-matter coupling by emphasizing gauge invariance and cavity bath effects, revealing differences in models with and without classical analogues.

Contribution

It introduces the importance of gauge corrections and cavity bath coupling in quantum models to align spectral predictions with classical theories in ultrastrong coupling regimes.

Findings

Quantum and classical spectra align when gauge invariance is maintained.

Cavity bath coupling significantly affects the quantum Rabi model's spectrum.

Classical analogue exists only under specific quantum model conditions.

Abstract

Focusing on the widely adopted Hopfield model with cavity dissipation, we show how the linear spectrum of an ultrastrongly coupled cavity and a dipole can be described either classically or quantum mechanically, but only when the quantum model includes (i) corrections to maintain gauge invariance, and (ii) a specific type of cavity bath coupling. We also show the impact of this bath model on the quantum Rabi model, which has no classical analogue in ultrastrong coupling.