Synchronization in microwave optomechanical circuits via coupling engineering to a common environment

Synchronization is one of the essential collective behaviors and has extensive applications. Exploiting a common environment, we establish synchronization in microwave optomechanical circuits. Through analysis and numerical calculations, we study the synchronization dynamics of three nonidentical and mechanically isolated optomechanical resonators. Each resonator supports a microwave mode and a mechanical mode, which are coupled via radiation-pressure type optomechanical interaction. The common environment induces indirect coupling between any two resonators, which can be described by an effective non-Hermitian interaction Hamiltonian. Combined with the Hermitian interaction regulated by the tunable coupler, we demonstrate that the common environment breaks the reciprocity of the interaction. We propose several special microwave optomechanical circuits with nonreciprocal or even unidirectional interactions, and study the regulation of synchronization dynamics by the common environment. By utilizing the excellent tunability of superconducting circuits, we show that different synchronization states can be switched in a controllable way. This work may open up a new way for synchronization research and have potential applications in synchronization networks.