Chiral Waveguide Optomechanics: First Order Quantum Phase Transitions with Z3 Symmetry Breaking

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 we 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 Z₃ rather than parity Z₂ symmetry and demonstrate the emergence of the multicomponent Schrödinger-cat ground states in these systems.