Turing instability of activator-inhibitor units in open quantum systems*

We show that Turing instability, a fundamental mechanism of nonequilibrium self-organization in classical systems, can also occur in a open quantum system. We propose a degenerate parametric oscillator with nonlinear damping in quantum optics as a quantum activator–inhibitor unit and numerically demonstrate that a system of two such units can undergo Turing instability when diffusively coupled with each other. We also show that the Turing instability induces nonuniformity and entanglement between the two units and gives rise to a pair of nonuniform states that are mixed due to quantum noise. We further show that performing continuous measurement on the coupled system reveals the true asymmetry caused by the Turing instability. Our results extend the universality of the Turing mechanism to the quantum realm and may provide a novel perspective on the possibility of quantum nonequilibrium self-organization.