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

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.

Source: arXiv:2604.14052v1 - http://arxiv.org/abs/2604.14052v1 PDF: https://arxiv.org/pdf/2604.14052v1 Original Link: http://arxiv.org/abs/2604.14052v1