Tripartite optomechanical entanglement via optical-dark-mode control

We propose how to generate a tripartite light-vibration entanglement by controlling an optical dark mode (ODM), which is induced by the coupling of two optical modes to a common vibrational mode. This ODM is decoupled from the vibration, and it can be controlled on demand by employing a synthetic gauge field, which can enable efficient switching between the ODM-unbreaking and ODM-breaking regimes. We find that the tripartite optomechanical entanglement is largely suppressed in the ODM-unbreaking regime, but it is significantly enhanced in the ODM-breaking regime. In particular, the noise robustness of quantum entanglement in the ODM-breaking regime can be more than twice than that in the ODM-unbreaking regime. This study offers a method for protecting and enhancing fragile quantum resources and for constructing noise-tolerant and dark-mode-immune quantum processors and entangled networks.