The simultaneous ground-state cooling of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity-field mode has become an outstanding challenge in cavity optomechanics. This is because the dark modes formed by these mechanical modes decouple from the cavity mode and prevent extracting energy from the dark modes through the cooling channel of the cavity mode. Here we propose a universal and reliable dark-mode-breaking method to realize the simultaneous ground-state cooling of two degenerate or nondegenerate mechanical modes by introducing a phase-dependent phonon-exchange interaction, which is used to form a loop-coupled configuration. We find an asymmetrical cooling performance for the two mechanical modes and expound this phenomenon based on the nonreciprocal energy transfer mechanism, which leads to the directional flow of phonons between the two mechanical modes. We also generalize this method to cool multiple mechanical modes. The physical mechanism in this cooling scheme has general validity and this method can be extended to break other dark-mode and dark-state effects in physics.

中文翻译：

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多个机械谐振器的不可逆基态冷却

耦合到公共腔场模式的多个简并或近简简机械模式的同时基态冷却已成为腔体光力学中的一项严峻挑战。这是因为由这些机械模式形成的暗模式与腔模式解耦，并且阻止了通过腔模式的冷却通道从暗模式提取能量。在这里，我们提出了一种通用且可靠的暗模式破坏方法，通过引入依赖于相位的声子交换相互作用来实现两个简并或非简并机械模式的同时基态冷却，该方法用于形成回路耦合配置。我们发现两种机械模式的冷却性能不对称，并基于不可逆的能量传递机理阐述了这种现象，这导致声子在两种机械模式之间的定向流动。我们还推广了这种方法来冷却多种机械模式。该冷却方案中的物理机制具有普遍的有效性，可以扩展此方法以打破物理中的其他暗模式和暗状态效应。