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

Abstract

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.

There are some incorrect descriptions in the Methods part of the manuscript, so we would like to withdraw this manuscript and do some further revisions