Quantum $\ddot{I}†$-synchronization in coupled optomechanical system with periodic modulation

Abstract

Based on the concepts of quantum synchronization and quantum phase synchronization proposed by A. Mari \textit{et al.} in Phys. Rev. Lett. 111, 103605 (2013), we introduce and characterize the measure of a more generalized quantum synchronization called quantum $\ddot{I}†$-synchronization under which the pairs of variables have the same amplitude and possess the same $\ddot{I}†$ phase shift. Naturally, quantum synchronization and quantum anti-synchronization become special cases of quantum $\ddot{I}†$-synchronization. Their relations and differences are also discussed. To illustrate these theories, we investigate the quantum $\ddot{I}†$-synchronization and quantum phase synchronization phenomena of two coupled optomechanical systems with periodic modulation and show that quantum $\ddot{I}†$-synchronization is more general as a measure of synchronization. We also show the phenomenon of quantum anti-synchronization when $\ddot{I}†=\ddot{I}€$.

6 pages, 5 figures, comments are wellcome