论文标题
多频驱动系统中可控的浮光边缘模式
Controllable Floquet edge modes in a multi-frequency driving system
论文作者
论文摘要
最近在非平衡相变及其响应的背景下研究了一个驱动的量子系统。特别是,对于定期驱动的系统,其动力学是根据晶格大小的多维浮子晶格描述的,具体取决于驾驶频率的数量及其合理或不合理比率。到目前为止,对于多频驱动系统,频率来源之间的能量泵送已被广泛讨论为拓扑非平凡的浮标带的签名。但是,尚未探索在浮标晶格中出现的独特边缘模式。在这里,我们讨论了如何控制floquet晶格中的边缘模式,并在存在多个频率的情况下在特定频率下定位,并且它们的幅度是相称的值。首先,我们构建了最小模型来体现我们的论点,重点是具有两个驱动频率的两级系统。对于强频限制,人们可以将系统描述为一个准尺寸浮子晶格,其中相邻位点之间的有效跳跃取决于两种频率模式的潜力的相对幅度。使用多个驾驶模式,总是存在通过控制频率的非平凡浮子晶格边界,这产生了大多数位于此类浮子晶格边界的状态,即特定的频率。我们建议使用时间依赖的克鲁兹梯子模型作为我们理论上的哈密顿式的实现,并显示了可控的浮雕边缘模式的出现。
A driven quantum system has been recently studied in the context of nonequilibrium phase transitions and their responses. In particular, for a periodically driven system, its dynamics are described in terms of the multi-dimensional Floquet lattice with a lattice size depending on number of driving frequencies and their rational or irrational ratio. So far, for a multi-frequency driving system, the energy pumping between the sources of frequencies has been widely discussed as a signature of topologically nontrivial Floquet bands. However, the unique edge modes emerging in the Floquet lattice has not been explored yet. Here, we discuss how the edge modes in the Floquet lattice are controlled and result in the localization at particular frequencies, when multiple frequencies are present and their magnitudes are commensurate values. First, we construct the minimal model to exemplify our argument, focusing on a two-level system with two driving frequencies. For strong frequency limit, one can describe the system as a quasi-one dimensional Floquet lattice where the effective hopping between the neighboring sites depends on the relative magnitudes of potential for two frequency modes. With multiple driving modes, there always exist the non-trivial Floquet lattice boundaries via controlling the frequencies and this gives rise to the states that are mostly localized at such Floquet lattice boundaries, i.e. particular frequencies. We suggest the time-dependent Creutz ladder model as a realization of our theoretical Hamiltonian and show the emergence of controllable Floquet edge modes.