Topological many-body phases of bosons and fermions in driven optical lattices

自量子霍尔效应发现以来，拓扑学已经成为量子物质分类的核心概念，通过对称性破缺描述了分类之外的奇异量子相。持续的兴趣是燃料的发现过多的影响和潜在的应用计量学和拓扑量子计算。在光学晶格中使用超冷原子的拓扑物质的量子模拟已经成功地使用Floquet驱动来设计电荷中性粒子的人工规范场，从而实现了范式拓扑模型。将联合收割机规范场与可调和强相互作用结合起来的可能性是实现相互作用拓扑物质（如分数陈氏绝缘体）的核心，而冷原子实验的出色可控性有望帮助建立对这些阶段的全面理解。汉堡团队开创了例如Floquet驱动的光晶格规范场，并首次实现了完整的动量-解决了Berry曲率的测量，并在研究单位内通过动态链接数和圆二色性首次测量陈数。此外，该团队还引入了机器学习技术，以改进拓扑相变的识别。在第二个资助期内，汉堡项目将以这些技术为基础，研究拓扑结构和弱相互作用和强相互作用机制中的相互作用。我们将准备和表征多体相位的玻色子和费米子在拓扑能带结构都在平衡和通过动力学淬火后。我们将实现一个六边形超晶格，这是至关重要的分数填充的准备，但也允许研究拓扑三带模型驱动光学Kagome晶格。此外，我们将实现准无序和研究的相互作用与拓扑结构和相互作用，期望观察到拓扑保护对无序和二维拓扑安德森绝缘体。汉堡项目将与研究股的理论项目和实验项目密切合作，直接比较实验结果和数值计算，并确定实现和表征奇异拓扑相的适当协议。

Since the discovery of the quantum Hall effect, topology has emerged as a central concept for the classification of quantum matter, describing exotic quantum phases beyond the classification via symmetry breaking. The persistent interest is fueled by the discovery of a plethora of effects and by potential applications in metrology and topological quantum computation. Quantum simulation of topological matter using ultracold atoms in optical lattices has become successful using Floquet driving to engineer artificial gauge fields for charge-neutral particles, leading to the realization of paradigmatic topological models. The possibility to combine gauge fields with tunable and strong interactions is at the heart of realizing interacting topological matter such as fractional Chern insulators, and the excellent controllability of cold atom experiments promises to help establishing a comprehensive understanding of these phases.The Hamburg team pioneered e.g. Floquet driven gauge fields in optical lattices and realized for the first time a full momentum-resolved measurement of the Berry curvature, and within the Research Unit the first measurement of the Chern number via the dynamical linking number and via circular dichroism. Furthermore, the team introduced the use of machine learning techniques for an improved identification of topological phase transitions.In the second funding period, the Hamburg project will build on these techniques and will study the rich interplay of topology and interactions both in the weakly- and in the strongly-interacting regimes. We will prepare and characterize many-body phases of bosons and fermions in topological band structures both in equilibrium and via dynamics after quenches. We will implement a hexagonal superlattice, which is vital for the preparation of fractional fillings, but also allows studying topological three-band models in driven optical Kagome lattices. Furthermore, we will implement quasi-disorder and study the interplay with topology and interactions, expecting to observe both topological protection against disorder and 2d topological Anderson insulators. The Hamburg project will strongly collaborate with the theory projects and experimental projects of the Research Unit on both a direct comparison between experimental results and numerical calculations and on the identification of suitable protocols for realizing and characterizing exotic topological phases.