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 Z(3) rather than parity Z(2) symmetry and demonstrate the emergence of the multicomponent Schrodinger-cat ground states in these systems.