Manipulating multiple optical parametric processes in photonic topological insulators

Topological quantum optics has endowed integrated quantum devices with novel functionalities, including unidirectional transport and immunity to structural defects. Here we propose topological interfaces that support two distinct edge modes with different frequency ranges. The nonlinear four-wave mixing processes in the topological interfaces lead to the generation of signal and idler photons, each corresponding to distinct edge modes. By designing a diamondlike topological structure, we can couple the signal and idler photons into opposite branches, leading to spatial separation of the photon pairs. This behavior enables on-chip generation and flexible control of the topological biphoton states. More importantly, the biphoton states are inborn topologically protected, showing robustness against sharp bends and disorders. Our proposal offers the possibility of robust, multifunctional topological quantum devices, which may find applications in quantum information processing.