Emergent Quantum Synchronization Without Symmetry Breaking

Abstract

Parametric amplification of a shared cavity mode turns the light--matter coupling phase of a two-ensemble Dicke model into a control parameter. We prove analytically that a cavity-set gain band opens a window of this phase with no static superradiant instability, leaving only a Hopf bifurcation, for arbitrary couplings, spin frequencies, damping rates and ensemble sizes. A ${\mathbb{Z}}_2$ parity keeps the quantum steady state unique and time independent: every order parameter vanishes and the oscillation lives in a slow parity-odd Liouvillian mode. Truncated-Wigner simulations, validated against exact ones, show that above threshold its quality factor grows linearly with system size and the ensembles phase lock; below threshold, both saturate. Quantum synchronization emerges without symmetry breaking and without requiring entanglement.