We propose a novel approach for microwave and optical fields entanglement using an electrical capacitor loaded with graphene plasmonic waveguide. In the proposed scheme, a quantum microwave signal of frequency f_m drives the electrical capacitor, while an intensive optical field (optical pump) of frequency f_1 is launched to the graphene waveguide as surface plasmon polariton (i.e., SPP) mode. The two fields interact by the means of electrically modulating the graphene optical conductivity. It then follows that an upper and lower SPP sideband modes (of f_2 = f_1 + f_m and f_3 = f_1 -f_m frequencies, respectively) are generated. We have shown that the microwave signal and the lower sideband SPP mode are entangled, given a proper optical pump intensity is provided. A quantum mechanics model is developed to describe the fields evolution. The entanglement of the two fields is evaluated versus many parameters including the waveguide length, the pump intensity, and the microwave frequency. We found that the two fields are entangled over a vast microwave frequency range. Furthermore, our calculations show that a significant number of entangled photons are generated at the lower SPP sideband. The proposed scheme attains tunable mechanism for microwave-optical entanglement which paves the way for efficient quantum systems.
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