Self-induced manipulation of biphoton entanglement in topologically distinct modes

TL;DR

The paper tackles the challenge of robust, programmable manipulation of biphoton entanglement in topological photonic lattices by engineering a defected SSH lattice with Kerr-type nonlinearities and pump-dependent inter-site coupling, leading to a time-dependent Hamiltonian $H(t)$. The authors decompose the system into a nonlinear coupling term $H_{nonlinear}$ and a biphoton generation term $H_{is}$ (with SFWM) and show how pump power can transform defect topology, creating pump-induced trivial modes that participate in biphoton generation. They demonstrate that the weight of topological biphoton states increases at intermediate pump powers and then decreases as the defect broadens, with robustness to moderate off-diagonal disorder; they also propose a time-bin photonic platform and an active, feedback-controlled realization for experimental demonstration. The results offer a scalable, reconfigurable path toward fault-tolerant quantum information processing using topology-protected entangled photons in integrated and time-bin photonic platforms.

Abstract

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.

Figures (7)

• Figure 1: The waveguide design. The pump light is injected at the left side of the center of the waveguides, with the propagation direction indicated by the yellow arrow (indexed as $-1$). The generated biphoton is indicated by the green and red arrows.
• Figure 2: (a),(b) Pump and (c),(d) biphoton dynamics in a 103-waveguides chip with a long-long defect centered at the waveguide indexed 0, with different pump power injections: (a),(c) 1 and (b),(d) 30.
• Figure 3: The pump spectrum at the last step of the evolution, where the pump is injected into the waveguide indexed $-1$ of a 103-waveguides chip with a long-long defect centered at the waveguide indexed 0.
• Figure 4: Eigenstate distribution of the pump model in 103 waveguides with a long-long defect with various pump power at the first and last step of the evolution, and the pump light is injected at the site $-1$. The initial pump power is set as (a)--(c) 1, (d)--(f) 30, and (g)--(i) 100. (a),(d),(g) The corresponding system spectrum. (b),(e),(h) The zero-energy, maximum-energy, and minimum-energy eigenmode distribution over the lattice at the first step of the evolution. (c),(f),(i) The zero-energy, maximum-energy and minimum-energy eigenmode distribution over the lattice at the last step of the evolution.
• Figure 5: (a) Heat map of the topological biphoton weight in the generated biphoton states concerning the pump power and evolution steps. (b) Heat map of the gap between the maximum eigenvalue and the bulk band in the time-dependent pump Hamiltonian spectrum with respect to the pump power and evolution steps.