From coupled $\mathbb{Z}_3$ Rabi models to the $\mathbb{Z}_3$ Potts model

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

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arXiv · 2604.14052

From coupled $\mathbb{Z}_3$ Rabi models to the $\mathbb{Z}_3$ Potts model

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

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Abstract

We study $\mathbb{Z}_3$-symmetric Rabi model that describes a three-level system coupled to two bosonic modes. We derive a mapping of the two-mode $\mathbb{Z}_3$ Rabi model onto a qubit-boson ring. This mapping allows us to formulate a realistic implementation of the $\mathbb{Z}_3$ Rabi model based on superconducting qubits. It also provides context for the previously proposed optomechanical implementation of the $\mathbb{Z}_3$ Rabi model. In addition, we propose a physical implementation of the $\mathbb{Z}_3$ Potts model via a coupled chain of $\mathbb{Z}_3$ Rabi models.

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Anatoliy I. Lotkov, Valerii K. Kozin, Denis V. Kurlov, Jelena Klinovaja, Daniel Loss. 2026-04-15. From coupled $\mathbb{Z}_3$ Rabi models to the $\mathbb{Z}_3$ Potts model. https://arxiv.org/abs/2604.14052

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