Spectral classification of coupling regimes in the quantum Rabi model

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.

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

“…If the coupling is small with respect to the resonator (atomic) frequency ω r (ω a ), g ω r ,ω a , and the frequencies respect the condition |ω a − ω r | |ω r + ω a |, the interaction is faithfully described with the Jaynes-Cummings (JC) model [3]. As the coupling becomes a considerable fraction of ω r or ω a , typicallyḡ = g/ω r,a ∼ 0.1, the JC model no longer applies and the interaction is better described by the Rabi model [4][5][6][7]. This ultrastrong coupling (USC) regime shows the breakdown of excitation number conservation; however, excitation parity remains conserved for arbitrarily largeḡ [8].…”

Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

“…Recent experimental achievements have shown the accessibility to the ultrastrong-coupling (USC) regime [15] or even to the deep strong-coupling (DSC) regime [16,17], where the coupling strength is comparable to or larger than the mode frequency. In these strong-coupling regimes, the RWA breaks down, rendering the JCM as a restricted description of the system, and requiring the use of the full QRM to correctly describe the emerging physical phenomena [18]. It is noteworthy to mention that, in such regimes, exotic dynamical properties of lightmatter interaction [19] and potential applications to quantum information technologies [20] have been predicted and proposed.…”

Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

“…In the USC regime, even * louis.garbe@ens-lyon.fr apparently simple models entail a very complex physics. This is the case for the quantum Rabi model [35,36], which corresponds to a single-qubit DM. Furthermore, the engineering of effective Hamiltonians allows to implement generalized quantum optical models [37,38], including anisotropic couplings or two-photon interactions.…”