Spectral Classification of Coupling Regimes in the Quantum Rabi Model

TL;DR

This paper introduces a spectral classification of coupling regimes in the quantum Rabi model, dividing them into three regions based on perturbative criteria, which clarifies their physical properties and dynamical behaviors.

Contribution

It proposes a novel spectral classification scheme for the quantum Rabi model's coupling regimes, incorporating energy access and providing insights into static and dynamic properties.

Findings

Identifies three distinct coupling regimes with spectral criteria.

Shows the dependence of regimes on energy access and coupling ratios.

Explains collapse and revival phenomena within the classification.

Abstract

The quantum Rabi model is in the scientific spotlight due to the recent theoretical and experimental progress. Nevertheless, a full-fledged classification of its coupling regimes remains as a relevant open question. We propose a spectral classification dividing the coupling regimes into three regions based on the validity of perturbative criteria on the quantum Rabi model, which allows us the use of exactly solvable effective Hamiltonians. These coupling regimes are i) the perturbative ultrastrong coupling regime which comprises the Jaynes-Cummings model, ii) a region where non-perturbative ultrastrong and non-perturbative deep strong coupling regimes coexist, and iii) the perturbative deep strong coupling regime. We show that this spectral classification depends not only on the ratio between the coupling strength and the natural frequencies of the unperturbed parts, but also on the energy to which the system can access. These regimes additionally discriminate the completely different behaviors of several static physical properties, namely the total number of excitations, the photon statistics of the field, and the cavity-qubit entanglement. Finally, we explain the dynamical properties which are traditionally associated to the deep strong coupling regime, such as the collapses and revivals of the state population, in the frame of the proposed spectral classification.