  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.
