Lyapunov-based quantum synchronization in designed optomechanical systems

TL;DR

This paper extends quantum synchronization concepts to generalized synchronization in optomechanical systems, using Lyapunov control theory and simple voltage controls, and explores the role of entanglement.

Contribution

It introduces a Lyapunov-based control method for quantum generalized synchronization in optomechanical systems, with a flexible control framework and entanglement analysis.

Findings

Lyapunov functions enable flexible control objectives.

Control fields can be implemented with simple time-variant voltages.

Quantum entanglement exists in various generalized synchronization regimes.

Abstract

We extend the concepts of quantum complete synchronization and phase synchronization, which are proposed firstly in [Phys. Rev. Lett, 111 103605 (2013)], to more widespread quantum generalized synchronization. The generalized synchronization can be considered as a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measurement are further proposed and analyzed in this paper. As an example, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling synchronization system, we purposefully design extra control fields based on Lyapunov control theory. We find that the Lyapunov function can adapt to more flexible control objectives, which is more suitable for generalized synchronization control, and the control fields can be achieved simply with a time-variant voltage. Finally, the existence of quantum entanglement in different generalized synchronizations is also discussed.