Manipulation of tunable nonreciprocal entanglement and one-way steering induced by two-photon driving

We consider an all-optical system consisting of two whispering-gallery-mode microring resonators and two adjacent optical waveguides. Pumping fields from different directions can simultaneously excite both clockwise and counterclockwise modes in the two resonators. When the propagation direction of the excited photons aligns with the propagation direction of the photons excited by two-photon driving, satisfying the phase-matching conditions, stable nonreciprocal quantum entanglement and one-way Einstein-Podolsky-Rosen (EPR) steering can be effectively generated. This work demonstrates that quantum correlations can only be prepared when the system is driven by a pumping field from the unique port, a condition induced by the nonlinearity of the system. Furthermore, we show that the maximum values of quantum entanglement and one-way EPR steering can be achieved when the frequency detunings of the two optical modes are opposite, and higher two-photon driving strength and coupling strength significantly enhance quantum entanglement and one-way EPR steering. Our study provides a highly manipulable platform, offering promise for one-way quantum computing and quantum communication based on macroscopic entangled states.