Entanglement of microwave-optical modes in a strongly coupled electro-optomechanical system

Quantum transduction between microwaves and optics can be realized by quantum teleportation if given reliable microwave-optical entanglement, namely, entanglement-based quantum transduction. To realize this protocol, an entangled source with a high fidelity between the two frequencies is necessary. In this paper, we study microwave and optical entanglement generation based on a generic cavity electro-optomechanical system in the strong coupling regime. Splittings are shown in the microwave and optical output spectra and the frequency entanglement between the two modes is quantified. We show that entanglement can be straightforwardly encoded in the frequency-bin degree of freedom and propose a feasible experiment to verify entangled photon pairs. The experimental implementation is systematically analyzed, and the preferable parameter regime for entanglement verification is identified. An inequality is given as a criterion for good entanglement verification with analysis of practical imperfections.