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arXiv:2604.20363

Jaynes-Cummings dynamics in strong coupling for many-interacting-qubit quantum Rabi models

Roberto Grimaudo, Sagnik Chakraborty, Rosario Lo Franco, Giuseppe Falci

quant-phSubmitted Apr 22, 2026• Announced Apr 23, 2026• 0 citations
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Abstract

The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an $N$-qubit chain quantum Rabi models.

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The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an NNN-qubit chain quantum Rabi models.
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.
he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summation of periodic cosine functions of the evolution.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
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 nonperturbative ultrastrong and nonperturbative 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 with the deep strong coupling regime, such as the collapses and revivals of the state population, in the frame of the proposed spectral classification.
The Jaynes-Cummings and quantum Rabi models are fundamental to cavity and circuit quantum electrodynamics, as they describe the simplest form of light-matter interaction, where a single qubit is coupled to a single bosonic mode. A scenario that is commonly encountered in the experimental practice arises when the bosonic mode interacts with an external dissipative thermal bath, making the qubit-boson system open. In this work, we present a new analytical solution of the Lindblad master equations for the open dispersive Jaynes-Cummings model and a perturbative analytical solution of the open quantum Rabi model in the limit of weak qubit-boson coupling ggg, using the holomorphic formalism in Bargmann space. Specifically, we derive the most general solution of the local Lindblad master equation for the open dispersive Jaynes-Cummings model coupled to a thermal bath, with the only assumptions that the initial state of the qubit-boson system is separable. Additionally, we obtain a perturbative analytical solution for the open quantum Rabi model up to second order in ggg. Notably, our findings include a new formula for the qubit's steady state at zeroth order, showing that the stationary populations depend on both qubit and boson frequencies in the quantum Rabi model, but not in the Jaynes-Cummings model, regardless of the value of ggg. Our results are of general interest to the study of open quantum systems in the context of light-matter interaction.