Topological Photon Transport in Programmable Photonic Processors via Discretized Evolution of Synthetic Magnetic Fields

Abstract: Photons, unlike electrons, do not couple directly to magnetic fields, yet synthetic gauge fields can impart magnetic-like responses and enable topological transport. Discretized Floquet evolution provides a controlled route, where the time-ordered sequencing of non-commuting Hamiltonians imprints complex hopping phases and breaks time-reversal symmetry. However, stabilizing such driven dynamics and observing unambiguous topological signatures on a reconfigurable platform has remained challenging. Here we demonstrate synthetic gauge fields for light on a programmable photonic processor by implementing discretized Floquet drives that combine static and dynamic phases. This approach reveals hallmark features of topological transport: chiral circulation that reverses under drive inversion, flux-controlled interference with high visibility, and robust directional flow stabilized by maximizing the minimal Floquet quasi-energy gap. The dynamics are further characterized by a first-harmonic phase order parameter, whose per-period winding number quantifies angular drift and reverses sign with the drive order. These results establish discretized, gap-optimized Floquet evolution as a versatile and fully programmable framework for topological photonics, providing a compact route to engineer gauge fields, stabilize driven phases, and probe winding-number signatures of chiral transport.