Self-induced manipulation of biphoton entanglement in topologically distinct modes

Biphoton states have shown promising applications in quantum information processing, including quantum communications, quantum metrology, and quantum imaging. The generation and manipulation of biphoton entanglement in topologically distinct modes paves the way in this direction. Here we present a comprehensive method for regulating the topological properties of the system by combining the nonlinearity in waveguides, i.e., nonlinearity in the waveguide coupling materials, and the waveguide lattice structure. Our method enables the generation of topological biphoton states with injected pump activation on the topologically trivial modes. This is realized through self-induced manipulation on pump-dependent nonlinear couplings on the defects, which is unable to be realized while there are no such nonlinear couplings. Specifically, by including the nonlinear gain/loss mechanism in the coupling between the nearest-neighbor waveguides and the third-order Kerr nonlinearity effect along the waveguides, the injected pump power will be the controllable parameter for the manipulation of the topology in the defect states and the generation of biphoton entanglement states. We also present an experimental proposal to realize our scheme and its generalization in the contemporaneous ``active'' topological photonics time-bin platforms. Our method can be used in other Su-Schrieffer-Heeger (SSH) models with various defect configurations. Our method enables the reusability and versatility of SSH lattice chips and their application for fault-tolerant quantum information processing, promoting the industrialization process of quantum technology.