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Cat states in one- and two-mode Z3 Rabi models

Anatoliy I. Lotkov1,*, Denis V. Kurlov1, Valerii K. Kozin1, Jelena Klinovaja1, and Daniel Loss1,2,3,4

  • *Contact author: anatolii.lotkov@unibas.ch
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Phys. Rev. Research 8, 023152 – Published 11 May, 2026

DOI: https://doi.org/10.1103/bvk8-kxmy

Abstract

We investigate one- and two-mode variants of the Z3-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 Z3 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 Z3 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 Z3 qutrit-boson cat states.

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Phys. Rev. Research 8, 023152– Published 11 May, 2026
  • Received 22 September 2025
  • Accepted 25 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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