标题： 几何量子驱动：双曲驱动的量子系统及更广义的情况 显示英文标题

标题： Geometric quantum drives: Hyperbolically driven quantum systems and beyond

摘要： 我们提出了一种驱动量子系统的几何构造，其中在光滑连通流形上自主运动的经典粒子的位置被用来随时间调节量子哈密顿量。 这导致了一个具有结构化时间轮廓的时变量子哈密顿量，其性质取决于所选流形的局部和全局特性。 我们解释了我们的构造如何恢复已知的周期性驱动和准周期性驱动量子系统类别，但也揭示了根本新颖的量子动力学类别：通过使用在称为博尔扎曲面的紧致二维双曲黎曼表面上自由运动的经典粒子来调节量子哈密顿量，我们展示了双曲驱动量子系统的例子。 我们证明了在绝热极限下完全带隙的双曲驱动量子系统由一个量化动力响应进行拓扑分类。 我们提出几何量子驱动作为一个通用框架，用于绘制时变量子系统的景观，这可以在现代量子模拟器中可用的时间依赖控制下实现。 显示英文摘要

摘要： We present a geometrical construction of driven quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time. This results in a time-dependent quantum Hamiltonian with a structured temporal profile and properties dependent on the local and global nature of the underlying choice of manifold. We explain how our construction recovers the well-known classes of periodically-driven and quasiperiodically-driven quantum systems, but also unveils fundamentally novel classes of quantum dynamics: by steering a quantum Hamiltonian using a classical particle freely moving on a compact 2d hyperbolic Riemann surface called the Bolza surface, we demonstrate an example of a hyperbolically driven quantum system. We show that fully gapped hyperbolically driven quantum systems in the adiabatic limit are topologically classified by a quantized dynamical response. We propose geometric quantum driving to be a general framework to chart the landscape of time-dependent quantum systems, which can be realized with time-dependent controls available in modern day quantum simulators.