Entanglement of Microwave and Optical Fields using Electrical Capacitor Loaded with Plasmonic Graphene Waveguide

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 ${\omega_{m}}$ drives the electrical capacitor, while an intensive optical field (optical pump) of frequency ${\omega_{1}}$ is launched to the graphene waveguide as a 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 ${\omega_{2}=\omega_{1}+\omega_{m}}$ and ${\omega_{3}=\omega_{1}-\omega_{m}}$ frequencies, respectively) are generated. We show that the microwave signal and the lower sideband SPP mode are entangled, for a proper optical intensity. A quantum mechanics model is carried out to describe the fields evolution. Furthermore, novel iterative approach (based on combining the Duan criterion with the quantum regression theorem) is developed to assess the fields entanglement. Consequently, the entanglement of the two fields is evaluated versus several parameters including the waveguide length, the pump intensity, and the microwave frequency. We find that the two fields are entangled over a vast microwave frequency range. Moreover, 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.