Nonreciprocal Quantum Entanglement Against Backscattering

We propose how to achieve nonreciprocal optomechanical entanglement in a spinning resonator and maintain its quality against backscattering losses. We find that by splitting the counter-propagating optical modes in the resonator via the Sagnac effect, photon-phonon entanglement can be created from one side while prohibited from the other--that is, achieving quantum nonreciprocity in such a system. An important and counterintuitive feature of the nonreciprocal entanglement is its robustness against backscattering losses induced by impurities or material imperfections in practical devices. Building a new bridge between quantum control and nonreciprocal physics, our work reveals a new strategy to protect quantum entanglement which has applications in such a wide range of fields as backaction-immune quantum metrology and chiral quantum information networks.