The paradigm of Floquet engineering of topological states of matter can be generalized into the time-quasiperiodic scenario, where a lower-dimensional time-dependent system maps onto a higher-dimensional one by combining the physical dimensions with additional synthetic dimensions generated by multiple incommensurate driving frequencies. Differently from most previous works in which gapped topological phases were considered, we propose an experimentally realizable, one-dimensional chain driven by two frequencies, which maps onto a gapless Weyl semimetal in a synthetic dimension. Based on analytical reasoning and numerical simulations, we find that the nonadiabatic quantum dynamics of this system exhibit energy pumping behaviors characterized by universal functions. We also numerically find that such behaviors are robust against a considerable amount of spatial disorder.

中文翻译：

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准周期驱动扩展系统中的通用非绝热能量泵送

物质拓扑状态的 Floquet 工程范式可以推广到时间准周期场景，其中通过将物理维度与由多个不相称驱动生成的附加合成维度相结合，低维时间依赖系统映射到高维系统频率。与之前考虑有间隙拓扑相的大多数工作不同，我们提出了一个由两个频率驱动的实验可实现的一维链，它映射到合成维度的无间隙外尔半金属上。基于分析推理和数值模拟，我们发现该系统的非绝热量子动力学表现出以通用函数为特征的能量泵浦行为。