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arXiv · 2509.08603

Cat states in one- and two-mode $\mathbb{Z}_3$ Rabi models

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

We investigate one- and two-mode variants of the $\mathbb{Z}_3$-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 $\mathbb{Z}_3$ 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 $\mathbb{Z}_3$ 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 $\mathbb{Z}_{3}$ qutrit-boson cat states.

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Anatoliy I. Lotkov, Denis V. Kurlov, Valerii K. Kozin, Jelena Klinovaja, Daniel Loss. 2025-09-10. Cat states in one- and two-mode $\mathbb{Z}_3$ Rabi models. https://arxiv.org/abs/2509.08603

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