Turing instability in quantum activator-inhibitor systems

TL;DR

This paper demonstrates that Turing instability, a key mechanism of self-organization, can occur in quantum dissipative systems, revealing quantum features like entanglement and measurement effects, thus extending classical concepts into the quantum domain.

Contribution

It introduces a quantum activator-inhibitor model exhibiting Turing instability, highlighting quantum-specific phenomena and measurement effects, expanding the understanding of self-organization in quantum systems.

Findings

Turing instability occurs in quantum dissipative systems.

Quantum entanglement arises from the instability.

Measurement reveals nonuniform quantum states.

Abstract

Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and analyze its quantum features such as entanglement and the effect of measurement. We propose a degenerate parametric oscillator with nonlinear damping in quantum optics as a quantum activator-inhibitor unit and demonstrate that a system of two activator-inhibitor units can undergo Turing instability when diffusively coupled with each other. 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. Further performing continuous measurement on the coupled system reveals the nonuniformity 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 and its application in quantum technologies.