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

TL;DR

This paper maps a three-level quantum system coupled to bosonic modes onto a qubit-boson ring, enabling realistic superconducting qubit implementations and connecting to the $ ext{Z}_3$ Potts model.

Contribution

It introduces a mapping of the $ ext{Z}_3$ Rabi model to a qubit-boson ring and proposes a physical realization of the $ ext{Z}_3$ Potts model.

Findings

Mapping of the $ ext{Z}_3$ Rabi model onto a qubit-boson ring.

Proposal for superconducting qubit implementation.

Physical realization of the $ ext{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.