Floquet engineering and control of topological optical-lattice systems

拓扑光学晶格系统的Floquet工程和控制

• 批准号: 318596207
• 负责人: Professor Dr. André Eckardt
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318596207?language=en
• 关键词: Floquet; engineering; control; topological; optical

Recently, we saw tremendous progress in realizing artificial magnetic fields and topological band structures in optical lattices. This led, inter alia, to the observation of a quantized Hall response, the measurement of Chern numbers from the far-from equilibrium dynamics, and the detection of chiral edge modes. These studies are motivated by the unique properties of atomic quantum gases, which are complementary to those of electronic systems. These include the possibility to cleanly realize highly tunable minimal lattice models,single-lattice-site resolution for measuring and manipulating atoms, and the ability to study coherent many-body dynamics given by theexcellent isolation in combination with the capability to manipulate these systems on their intrinsic time scales. The latter is also used forthe creation of strong artificial magnetic fields (of up to a flux quantum per plaquette) via time-periodic driving (Floquet engineering).Extending these studies to interacting topological systems, is an important goal, for which we will address the following problems:Disorder-induced (many-body) localization is proposed as a way to suppress driving-induced heating and can induce also topologicallynon-trivial states (topological Anderson insulators). These effects were described, however, using low-energy models. Their robustnessagainst heating via multi-photon transitions to excited lattice bands is an open question, which we wish to address. Another strategy tocounteract driving-induced heating is the coupling to a bath, given, e.g., by a second atomic species. Therefore, we will investigate open Floquet systems and their non-equilibrium steady states. To this end, we will work out, how to use efficient quantum-trajectory simulations also beyond the typical secular approximation for very weak systembath coupling, which is hard to justify for Floquet systems. It is one question, whether a certain topological state can be stabilized as ground-state of an (approximate) Floquet Hamiltonian. Of equal importance is, however, also how this state can be prepared and probed. We will, therefore, study optimal preparation protocols for fractional Chern insulators and schemes for probing their fractional quasiparticle statistics. This includes also the study of magnetic-field ramps, which, so far, have not been implemented in optical lattices.We will numerically investigate the impact of interactions on the measurement of topological invariants, including also the winding numbers that characterize anomalous Floquet topological insulators beyond their Chern numbers. For an analytical description of these systems, we will also employ flow equations in Floquet space. Finally, we plan to derive lattice models for the recently proposed traid anyons and work out schemes for their quantum-gas implementation via engineering. We will pursue these goals in close collaboration with other experimental and theory teams of the Research Unit.

最近，我们看到了在光学晶格中实现人工磁场和拓扑带结构方面的巨大进展。除此之外，这导致了量化的霍尔响应的观察，远距离平衡动力学的Chern数量的测量以及手性边缘模式的检测。这些研究是由原子量子气体的独特特性激励的，原子量子气体与电子系统的互补。其中包括可以清洁可调的最小晶格模型，用于测量和操纵原子的单个晶格位点的分辨率，以及研究由脱离隔离的能力，以及能够在其本质时间范围内操纵这些系统的能力。后者还用于通过时间周期驾驶（Floquet Engineering）创建强大的人造磁场（每个plaquette的通量量子）。将这些研究扩展到相互作用的拓扑系统，这是一个重要的目标，我们将为我们解决以下问题：解决方案（许多身体）的定位，并抑制了诱导的诱因 - 诱导的助产（诱导了诱导的暖度），这是一种问题。安德森绝缘子）。但是，使用低能模型描述了这些效果。他们通过多光子向激发晶格带的多光量过渡加热的坚固加热是一个悬而未决的问题，我们希望解决。另一个策略引起的驱动引起的加热是与浴的耦合，例如第二个原子物种。因此，我们将研究开放式浮雕系统及其非平衡稳态。为此，我们将解决如何使用高效的量子 - 区域性模拟，这也是超出典型的世俗近似值，以实现非常弱的Systembath耦合，这对于Floquet Systems来说很难证明是合理的。这是一个问题，是否可以将某个拓扑状态稳定为（近似）浮雕哈密顿式的地面。但是，同等重要的是如何准备和探测该状态。因此，我们将研究用于探测其分数准粒子统计的分数绝缘子和方案的最佳制备方案。这还包括对磁场坡道的研究，到目前为止尚未在光学晶格中实施。我们将在数值上研究相互作用对拓扑不变式测量的影响，包括表征异常的浮质拓扑拓扑绝缘子，超出其Chern数字。对于这些系统的分析描述，我们还将在Floquet空间中采用流动方程。最后，我们计划为最近提议的Traid Anyons推导晶格模型，并通过工程制定其量子气实施方案。我们将与研究部门的其他实验和理论团队密切合作实现这些目标。