Opt Lett. 2018 Jun 15;43(12):2852-2855. doi: 10.1364/OL.43.002852.
In the linear response theory, it is well known that the response of a quantum system to an external perturbation described by the susceptibility is formulated in the Schrödinger picture. The theory might apply to open quantum systems (or Floquet systems); however, it has ignored the non-Markovian effect in almost all works so far. In this Letter, we propose a new method to address those issues by introducing Heisenberg operators to derive an exact susceptibility for the non-Markovian Floquet periodic driving system. The susceptibility includes all the influences of the environment on the Floquet system. We will show that the susceptibility connects closely to the structure of the Floquet energy spectrum of the whole system (system plus environment). Moreover, we can read out Floquet bound states in the first Brillouin zone of the whole system from the susceptibility. The presented results may find applications in quantum engineering with open systems following modulated periodic evolution in quantum optics.
在线性响应理论中，众所周知，用磁化率来描述的外场对量子系统的响应是在薛定谔绘景中表述的。该理论可能适用于开放量子系统（或 Floquet 系统）；然而，到目前为止，它几乎忽略了所有非马尔可夫效应。在这封信中，我们通过引入海森堡算子来解决这些问题，提出了一种新的方法，为非马尔可夫 Floquet 周期性驱动系统推导出一个精确的磁化率。磁化率包括环境对 Floquet 系统的所有影响。我们将表明，磁化率与整个系统（系统加环境）的 Floquet 能谱结构密切相关。此外，我们可以从磁化率中读出整个系统第一布里渊区中的 Floquet 束缚态。所提出的结果可能在量子光学中调制周期演化的开放系统的量子工程中有应用。
