Nonreciprocal entanglement in a molecular optomechanical system

We propose a theoretical scheme to generate nonreciprocal bipartite entanglement between a cavity mode and vibrational modes in a molecular cavity optomechanical system. Our system consists of $\mathcal{N}$ molecules placed inside a spinning whispering-gallery-mode (WGM) resonator. The vibrational modes of these molecules are coupled to the WGM resonator mode (which is analogous to a plasmonic cavity) and the resonator is also coupled to an auxiliary optical cavity. We demonstrate that nonreciprocal photon-vibration entanglement and nonreciprocal vibration-vibration entanglement can be generated in this system, even at high temperatures. These nonreciprocal entanglements arise due to the Sagnac-Fizeau effect induced by the spinning WGM resonator. We find that spinning the WGM resonator in the counter-clockwise (CCW) direction enhances both types of nonreciprocal entanglement, especially under blue-detuned driving of the optical cavity mode. Furthermore, we show that vibration-vibration entanglement can be significantly enhanced by increasing the number of molecules. Our findings have potential applications in quantum information transmission and in the development of nonreciprocal quantum devices.