标题： 二维Floquet拓扑相的噪声鲁棒性 显示英文标题

标题： Noise resilience of two-dimensional Floquet topological phases

摘要： 我们研究噪声对二维周期驱动拓扑相的影响，重点关注两个例子：异常弗洛凯-安德森相和无序弗洛凯-陈相。 这两个相在时间噪声下表现出意想不到的鲁棒性。 初始填充的拓扑边缘模态的噪声诱导衰减分为两个阶段：在较短时间尺度上，边缘模态之间的热化导致指数衰减。 随后是缓慢的代数衰减 $\sim n^{-1/2}$，随着弗洛凯循环次数 $n$而变化。 $1/2$的指数特征为一维扩散，在这里沿着边缘垂直方向发生。 相比之下，体内的局域模态表现出更快的衰减， $\sim n^{-1}$，对应于二维扩散。 我们通过全规模数值模拟展示了这些行为，并利用基于现象学模型的分析结果支持我们的结论。 我们的发现表明，由于实验中不可避免地存在静态无序和退相干，二维弗洛凯拓扑相是弗洛凯拓扑潜在应用的理想候选者。 显示英文摘要

摘要： We study the effect of noise on two-dimensional periodically driven topological phases, focusing on two examples: the anomalous Floquet-Anderson phase and the disordered Floquet-Chern phase. Both phases show an unexpected robustness against timing noise. The noise-induced decay of initially populated topological edge modes occurs in two stages: At short times, thermalization among edge modes leads to exponential decay. This is followed by slow algebraic decay $\sim n^{-1/2}$ with the number of Floquet cycles $n$. The exponent of $1/2$ is characteristic for one-dimensional diffusion, here occurring along the direction perpendicular to the edge. In contrast, localized modes in the bulk exhibit faster decay, $\sim n^{-1}$, corresponding to two-dimensional diffusion. We demonstrate these behaviors through full-scale numerical simulations and support our conclusions using analytical results based upon a phenomenological model. Our findings indicate that two-dimensional Floquet topological phases are ideal candidates for potential applications of Floquet topology, given the unavoidable presence of both quenched disorder and decoherence in experiments.