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

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.

15 pages, 6 figures