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

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.