Periodically driven non-Hermitian quantum systems have become the center of interest in recent years due to their rich physical phenomena. In this work, we consider a one-dimensional non-Hermitian lattice model induced by partially asymmetric coupling with time-periodic and spatially periodic modulations upon on-site potentials. Within Floquet theorem, we obtain the Floquet quasienergy spectrum of this one-dimensional non-Hermitian system. We show that the robust zero-energy modes exist in the band gap from the real parts of quasienergy spectrum. Compared with the case of no modulations, two pairs of the conjugate imaginary parts are added, which can be attributed to the combined modulations upon the on-site potentials. With the increase of non-Hermitian degree, the imaginary parts of the spectra are enlarged. We also observe the dynamical characteristics that, for different kinds of tunneling amplitudes between lattices, the amplitude of evolution gradually either decays to zero or eventually stabilizes at one particular value. Our protocol, possible to realize in photonic lattices, may facilitate the engineering of novel Floquet topological phases in non-Hermitian systems.

中文翻译：

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非厄米 Floquet 一维格模型的 Floquet 谱和动力学

近年来，周期性驱动的非厄米量子系统因其丰富的物理现象而成为人们关注的焦点。在这项工作中，我们考虑了由部分不对称耦合与现场电位的时间周期和空间周期调制引起的一维非厄米晶格模型。在 Floquet 定理中，我们得到了这个一维非 Hermitian 系统的 Floquet 准能谱。我们表明，在准能谱实部的带隙中存在稳健的零能量模式。与没有调制的情况相比，增加了两对共轭虚部，这可以归因于对现场电位的组合调制。随着非厄米度数的增加，谱的虚部扩大。我们还观察到动力学特性，对于不同类型的晶格间隧穿幅度，演化幅度逐渐衰减至零或最终稳定在一个特定值。我们的协议可以在光子晶格中实现，可以促进非厄米系统中新型 Floquet 拓扑相的工程。