Chiral waveguide optomechanics: first order quantum phase transitions with $\mathbb{Z}_3$ symmetry breaking/

TL;DR

This paper explores a novel quantum phase transition in chiral waveguide optomechanics, revealing multicomponent Schrödinger cat states and extending superradiant phase transition theory to systems with $ ext{Z}_3$ symmetry.

Contribution

It introduces a mapping between optomechanical systems and a generalized quantum Rabi model, extending superradiant phase transitions to $ ext{Z}_3$ symmetry and demonstrating multicomponent cat states.

Findings

Mapping between optomechanics and generalized Rabi model

Extension of superradiant phase transitions to $ ext{Z}_3$ symmetry

Emergence of multicomponent Schrödinger cat ground states

Abstract

We present a direct mapping between the quantum optomechanical problem of the atoms harmonically trapped in the vicinity of a chiral waveguide and a generalized quantum Rabi model and discuss the analogy between the self-organization of atomic chains in photonic structures and Dicke-like quantum phase transitions in the ultrastrong coupling regime. We extend the class of the superradiant phase transitions for the systems possessing $\mathbb{Z}_3$ rather than parity $\mathbb{Z}_2$ symmetry and demonstrate the emergence of the multicomponent Schrodinger cat ground states in these systems.