Synchronization has great impacts in various fields such as self-clocking, communication, and neural networks. Here, we present a mechanism of synchronization for two mechanical modes in two coupled optomechanical resonators with a parity-time ($\mathcal{PT}$)-symmetric structure. It is shown that the degree of synchronization between the two far-off-resonant mechanical modes can be increased by decreasing the coupling strength between the two optomechanical resonators due to the large amplification of optomechanical interaction near the exceptional point. Additionally, when we consider the stochastic noises in the optomechanical resonators by working near the exceptional point, we find that more noises can enhance the degree of synchronization of the system under a particular parameter regime. Our results open up a new dimension of research for $\mathcal{PT}$-symmetric systems and synchronization.

中文翻译：

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PT 对称光机械谐振器中的同步

同步在自时钟、通信、神经网络等各个领域都有很大的影响。在这里，我们提出了两个耦合光机械谐振器中两种机械模式的同步机制，具有奇偶校验时间（$\mathcal{PT}$)-对称结构。结果表明，由于异常点附近光机械相互作用的大放大，可以通过降低两个光机械谐振器之间的耦合强度来增加两个远谐振机械模式之间的同步程度。此外，当我们通过在异常点附近工作来考虑光机械谐振器中的随机噪声时，我们发现在特定参数范围内，更多的噪声可以增强系统的同步程度。我们的结果开辟了一个新的研究维度$\mathcal{PT}$-对称系统和同步。