We study Z3-symmetric Rabi model that describes a three-level system coupled to two bosonic modes. We derive a mapping of the two-mode Z3 Rabi model onto a qubit-boson ring. This mapping allows us to formulate a realistic implementation of the Z3 Rabi model based on superconducting qubits. It also provides context for the previously proposed optomechanical implementation of the Z3 Rabi model. In addition, we propose a physical implementation of the Z3 Potts model via a coupled chain of Z3 Rabi models.
@article{arxiv.2604.14052,
title = {From coupled $\mathbb{Z}_3$ Rabi models to the $\mathbb{Z}_3$ Potts model},
author = {Anatoliy I. Lotkov and Valerii K. Kozin and Denis V. Kurlov and Jelena Klinovaja and Daniel Loss},
journal= {arXiv preprint arXiv:2604.14052},
year = {2026}
}