Topological Hong-Ou-Mandel interference via compact edge modes

We propose a scheme based on synthetic-flux-induced topological edge modes for realizing Hong-Ou-Mandel (HOM) interference between spatial polarization modes in a long-period grating waveguide. By engineering the relative modulation phase of the gratings, a tunable synthetic magnetic flux is generated, enabling controlled conversion between the TE and TM modes and forming an effective mode lattice. At a flux of π, the coupled-waveguide system supports compact, highly localized topological edge modes. Harnessing these boundary states, we achieve HOM interference with near-unity visibility that is insensitive to propagation distance and robust against variations of the coupling coefficients. These results may provide a route for fault-tolerant on-chip photonic quantum circuits.