Preparation of entangled states of microwave photons in a hybrid system via the electro-optic effect

We propose to realize the two-mode continuous-variable entanglement of microwave photons in an electro-optic system, consisting of superconducting microwave resonators and optical cavities that are filled with certain electro-optic media. The cascaded and parallel schemes realize such entanglement via coherent control on the dynamics of the system, while the dissipative dynamical scheme utilizes the reservoir-engineering approach and exploits the optical dissipation as a useful resource. We show that, for all the schemes, the amount of entanglement is determined by the ratio of the effective coupling strengths of the "beam-splitter" and "two-mode squeezing" interactions, instead of their amplitudes.