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Exploring topological phases in quantum walks of twisted light

机译：探索扭曲光量子步态中的拓扑阶段

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摘要

Emerged as the quantum counterpart of classical random walks, quantum walks are established precious resources in a variety of quantum sciences. Recent studies have shown that quantum walks may be characterized by topological invariants, in close analogy to condensed matter systems exhibiting topological order. Exploiting these features, quantum walks are currently used to simulate topological systems and to probe their exotic features. Here we present the implementation of a one-dimensional quantum walk protocol based on the orbital angular momentum of light, manifesting the topological phases that characterize time-periodic systems (Floquet topological insulators) showing chiral symmetry. By considering the orbital angular momentum spectrum of a light beam undergoing this quantum evolution, we show that the associated statistical moments have marked differences in distinct phases and contain information on the system topology. While varying a control parameter determining the value of the invariants, these moments in the large step-number limit exhibit a sharp variation at the phase changes. We show that these phenomena arise from the singular behavior of the dispersion relation at the transition points. The extension of our results to systems featuring different symmetries, or characterized by higher spatial dimensions, may unveil novel intriguing features associated with these complex systems.
机译：作为经典随机游走的量子对应物出现，量子游走是各种量子科学中已建立的宝贵资源。最近的研究表明，量子行走的特征可能是拓扑不变性，与表现出拓扑顺序的凝聚态系统非常相似。利用这些特征，量子行走目前被用于模拟拓扑系统并探测其外来特征。在这里，我们介绍基于光的轨道角动量的一维量子步行协议的实现，体现了表征表现出手性对称性的时间周期系统（Floquet拓扑绝缘子）的拓扑相。通过考虑经历此量子演化的光束的轨道角动量谱，我们表明相关的统计矩在不同的相位上具有明显的差异，并且包含有关系统拓扑的信息。在改变确定不变式的值的控制参数的同时，这些大步数极限的力矩在相位变化时表现出急剧的变化。我们表明，这些现象是由色散关系在过渡点的奇异行为引起的。将我们的结果扩展到具有不同对称性或具有较高空间尺寸特征的系统，可能会揭示与这些复杂系统相关的新颖有趣的功能。

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