Robust quantized transport from topological quasienergy winding in long-range-coupling synthetic quantum walks

Quantized transport is a prominent feature in topological physics, with canonical examples being the quantum Hall effect and adiabatic Thouless pump, which are based on the Chern number, a topological invariant of 2D systems. Going beyond the Chern-number-based paradigms, quantized transports can also arise from k-direction quasienergy winding unique to periodically driven (Floquet) systems, which are free of dimensionality and adiabaticity limitations. However, lattices displaying winding of their quasienergy bands require asymmetric long-range couplings that are difficult to achieve in lattices of real-space coupled sites. Here, by leveraging photonic synthetic dimensions we construct asymmetric long-range-couplings in a one-dimensional temporal quantum walk based on three coupled fiber loops. We demonstrate quantized transport arising from the winding of quasienergy bands in k direction. We show that the average group velocity of an initial wave packet is proportional to the winding number, which leads to a quantized transport displacement. To better visualize this quantized displacement, we cascade two regions with flipped nearest/long-range couplings and observe a focusing effect with a quantized spatial shift in the focusing point. We also probe the robust properties of quantized transport against obstacles and disorders. The study initiates quasienergy-winding-based topological transports, which can feature applications in precise and robust imaging and information processing.