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arXiv:2509.08603 · Physical Review Research

Cat states in one- and two-mode Z 3 Rabi models

Anatoliy I. Lotkov, Denis V. Kurlov, Valerii K. Kozin, Jelena Klinovaja, Daniel Loss

Published Mar 25, 2026• 1 citation
arXivHTMLPDF

Abstract

We investigate one- and two-mode variants of the Z 3 -symmetric quantum Rabi model, which describe the interaction of a qutrit with one or two bosonic modes and are directly relevant for circuit-QED and spin-qudit platforms. We find a canonical transformation that allows one to obtain the spectrum of the Z 3 Rabi model using perturbation theory in a magnetic field. We show that in a certain parameter regime (deep-strong coupling and a small magnetic field), the three lowest eigenstates become Z 3 qutrit-boson cat states. In order to characterize these states, we introduce a joint qutrit-boson Wigner function and derive its closed-form expression for the qutrit-boson cat states. Numerical calculations across a wide range of coupling strengths show that the proposed Wigner function is a useful tool that allows one to unambiguously identify the states of the Z 3 qutrit-boson cat states.

DOI
10.1103/bvk8-kxmy

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We investigate one- and two-mode variants of the Z 3 -symmetric quantum Rabi model, which describe the interaction of a qutrit with one or two bosonic modes and are directly relevant for circuit-QED and spin-qudit platforms. We find a canonical transformation that allows one to obtain the spectrum of the Z 3 Rabi model using perturbation theory in a magnetic field. We show that in a certain parameter regime (deep-strong coupling and a small magnetic field), the three lowest eigenstates become Z 3 qutrit-boson cat states. In order to characterize these states, we introduce a joint qutrit-boson Wigner function and derive its closed-form expression for the qutrit-boson cat states. Numerical calculations across a wide range of coupling strengths show that the proposed Wigner function is a useful tool that allows one to unambiguously identify the states of the Z 3 qutrit-boson cat states.
We formulate and solve an effective spin-one quantum Rabi model motivated by the physical spin-one sector of the ten-component Duffin--Kemmer--Petiau (DKP) theory. After the constrained DKP components are separated from the three physical spin projections, the internal sector is represented as a qutrit. Under a single-mode and magnetic-dipole approximation, its coupling to a quantized electromagnetic field has the spin-one Rabi form g(a+a†)Sx. We derive the regular spectrum of this model in the Bargmann representation. The exact parity symmetry reduces the three-component problem to independent scalar three-term recurrences, from which parity-resolved spectral functions are obtained as continued fractions. The pole energies generated by eliminating the outer spin components are treated separately, allowing exceptional finite-polynomial states to be identified without confusing them with regular zeros of the continued fractions. Numerical comparison with direct Fock-space diagonalization confirms the regular spectral construction to better than 5×10−13 for a representative parameter set. The result establishes an exact spectral framework for a qutrit generalization of the quantum Rabi model and states explicitly the assumptions required for its connection with spin-one DKP dynamics.
We formulate and solve an effective spin-one quantum Rabi model motivated by the physical spin-one sector of the ten-component Duffin--Kemmer--Petiau (DKP) theory. After the constrained DKP components are separated from the three physical spin projections, the internal sector is represented as a qutrit. Under a single-mode and magnetic-dipole approximation, its coupling to a quantized electromagnetic field has the spin-one Rabi form g(a+a†)Sx. We derive the regular spectrum of this model in the Bargmann representation. The exact parity symmetry reduces the three-component problem to independent scalar three-term recurrences, from which parity-resolved spectral functions are obtained as continued fractions. The pole energies generated by eliminating the outer spin components are treated separately, allowing exceptional finite-polynomial states to be identified without confusing them with regular zeros of the continued fractions. Numerical comparison with direct Fock-space diagonalization confirms the regular spectral construction to better than 5×10−13 for a representative parameter set. The result establishes an exact spectral framework for a qutrit generalization of the quantum Rabi model and states explicitly the assumptions required for its connection with spin-one DKP dynamics.
Multi-qubit quantum Rabi model, which is a fundamental model describing light-matter interaction, plays an important role in various physical systems. In this paper, we propose a theoretical method to simulate multi-qubit quantum Rabi model in a circuit quantum electrodynamics system. By means of external transversal and longitudinal driving fields, an effective Hamiltonian describing the multi-qubit quantum Rabi model is derived. The effective frequency of the resonator and the effective splitting of the qubits depend on the external driving fields. By adjusting the frequencies and the amplitudes of the driving fields, the stronger coupling regimes could be reached. The numerical simulation shows that our proposal works well in a wide range of parameter space. Moreover, our scheme can be utilized to generate two-qubit gate, Schrödinger states, and multi-qubit GHZ states. The maximum displacement of the Schrödinger cat states can be enhanced by increasing the number of the qubits and the relative coupling strength. It should be mention that we can obtain high fidelity Schrödinger cat states and multi-qubit GHZ states even the system suffering dissipation. The presented proposal may open a way to study the stronger coupling regimes whose coupling strength is far away from ultrastrong coupling regimes.
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.
The interaction of a two-level system (TLS) with a single bosonic mode (BM) is one of the most fundamental processes in quantum optics. Microscopically, it is described by the quantum Rabi model (QRM). Here we propose a versatile implementation of this model based on single trapped cold atoms. Assuming realistic experimental conditions, we show that our approach is not restricted to the Jaynes-Cummings regime but also allows exploring the regimes of ultrastrong coupling, deep strong coupling, and dispersive deep strong coupling. In contrast to most other QRM platforms, all important system parameters, i.e., the emitter-field detuning and the coupling strength of the emitter to the mode, can be dynamically tuned over a wide range. The quantum state of the BM and the TLS can be prepared and read-out using standard cold-atom techniques, enabling the study of the QRM and its dynamics with unprecedented control. Our scheme implements the TLS using atomic Zeeman states, while the atom's vibrational states in the trap represent the BM. The coupling is mediated by a suitable fictitious magnetic field pattern. Finally, we show that our scheme also enables the implementation of important generalizations, namely, the driven QRM, the QRM with quadratic coupling, or the Dicke model.
We derive a quantum master equation in Lindblad form for the open quantum Rabi model in the perturbative deep strong coupling regime, where the spectrum is close to degenerate and harmonic. The Lindblad form is obtained by combining secular and singular-coupling approximations, working in a Schrieffer-Wolff transformed frame. We benchmark our equation against a Bloch-Redfield one, analyzing the time-evolution and steady state properties of several observables and find excellent agreement. Analytical results are obtained in limiting cases.