Entanglement of Microwave-Optical Modes in a Strongly Coupled Electro-Optomechanical System*

Quantum transduction between microwave and optics can be realized by quantum teleportation if given reliable entanglement between microwave and optical modes, namely entanglement-based quantum transduction. To realize this protocol, an entangled source with high-fidelity is necessary. Based on a generic strongly coupled cavity electro-optomechanical system, we study the microwave-optical entanglement generation and quantify the frequency entanglement between the two modes. The entanglement can be straightforwardly encoded in the frequency-bin degree of freedom with a feasible experiment to verify the entangled photon pairs. The experimental implementation is systematically analyzed, and the preferable parameter regime for entanglement verification is identied. An inequality is given as a criterion for good entanglement verification, including practical imperfections.

Part B: we theoretically evaluate the entanglement of formation rate, analyze Bell state violation and estimate the coincidence rate.