论文标题
Floquet Media中边缘状态的辐射衰减
Radiative decay of edge states in Floquet media
论文作者
论文摘要
我们考虑了具有拓扑保护的缺陷（边缘）模式的一维Schr {Ö} dinger方程的时间周期性强迫的效果。未强制的系统在周期性结构中模拟了域壁或位错缺陷，并支持一种缺陷模式，该缺陷模式从基础散装介质的Dirac点（线性频带交叉）分叉。我们研究了该状态在凝结物质，光子学和冷原子系统研究中产生的类型的时间周期性强迫的鲁棒性。我们的数值模拟表明，在足够高频率的时间周期性强迫下，缺陷状态会经历其能量的辐射泄漏，从界面移至整体。时间按在与强迫幅度的反平方成比例的时间尺度上的指数呈指数。我们的浮雕系统的包络动力学通过有效（同质化）定期造成的迪拉克方程来长时间尺度上大致控制。对有效包膜动力学的多尺度分析产生了辐射解决方案的扩展，这与我们的数值模拟非常一致。
We consider the effect of time-periodic forcing on a one-dimensional Schr{ö}dinger equation with a topologically protected defect (edge) mode. The unforced system models a domain-wall or dislocation defect in a periodic structure, and it supports a defect mode which bifurcates from the Dirac point (linear band crossing) of the underlying bulk medium. We study the robustness of this state against time-periodic forcing of the type that arises in the study of Floquet Topological Insulators in condensed matter, photonics, and cold-atoms systems. Our numerical simulations demonstrate that under time-periodic forcing of sufficiently high frequency, the defect state undergoes radiative leakage of its energy away from the interface into the bulk; the time-decay is exponential on a time-scale proportional to the inverse square of the forcing amplitude. The envelope dynamics of our Floquet system are approximately governed, on long time scales, by an effective (homogenized) periodically-forced Dirac equation. Multiple scale analysis of the effective envelope dynamics yields an expansion of the radiating solution, which shows excellent agreement with our numerical simulations.
