We propose a domino-cooling method to realize simultaneous ground-state cooling of a coupled mechanical-resonator chain through an optomechanical cavity working in the unresolved-sideband regime. This domino-effect cooling is realized by combining the cold-damping feedback on the first mechanical resonator with nearest neighbor couplings between other neighboring mechanical resonators. We obtain analytical results for the effective susceptibilities, noise spectra, final mean phonon numbers, and cooling rates of these mechanical resonators, and find the optimal cooling condition for these resonators. In particular, we analyze a two-mechanical-resonator case and find that by appropriately engineering either the laser power or the feedback, a flexible switch between symmetric and asymmetric ground-state cooling can be achieved. This could be used for preparing symmetric quantum states in multimode mechanical systems. We also simulate the cooling performance of a coupled $N$-mechanical-resonator chain and confirm that these resonators can be simultaneously cooled to their quantum ground states in the unresolved-sideband regime. Under proper parameter conditions, the cooling of the mechanical-resonator chain shows a temperature gradient along the chain. This study opens a route to quantum manipulation of multiple mechanical resonators in the bad-cavity regime.

中文翻译：

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通过冷阻尼反馈对耦合机械谐振器链进行多米诺冷却

我们提出了一种多米诺冷却方法，通过在未解析边带区域工作的光机械腔实现耦合机械谐振器链的同步基态冷却。这种多米诺效应冷却是通过将第一个机械谐振器上的冷阻尼反馈与其他相邻机械谐振器之间的最近邻耦合相结合来实现的。我们获得了这些机械谐振器的有效磁化率、噪声谱、最终平均声子数和冷却速率的分析结果，并找到了这些谐振器的最佳冷却条件。特别是，我们分析了两个机械谐振器的情况，发现通过适当地设计激光功率或反馈，可以实现对称和非对称基态冷却之间的灵活切换。这可用于在多模机械系统中制备对称量子态。我们还模拟了耦合的冷却性能$N$-机械谐振器链并确认这些谐振器可以在未解析的边带状态下同时冷却到它们的量子基态。在适当的参数条件下，机械谐振器链的冷却显示出沿链的温度梯度。这项研究为在坏腔状态下对多个机械谐振器进行量子操纵开辟了一条途径。