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

自从发现量子霍尔效应以来，拓扑学已经成为量子物质分类的中心概念，通过对称破缺描述了超越分类的奇异量子相。这种持续的兴趣是由大量效应的发现以及在计量学和拓扑量子计算中的潜在应用所推动的。利用光学晶格中的超冷原子对拓扑物质进行量子模拟已经取得成功，利用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。将规范场与可调谐强相互作用结合起来的可能性是实现诸如分数陈氏绝缘体等相互作用拓扑物质的核心，而冷原子实验的出色可控性有望帮助建立对这些相的全面理解。例如，汉堡团队率先在光学晶格中使用了Floquet驱动的规范场，并首次实现了Berry曲率的完全动量分辨测量，并且在研究单元内首次通过动态连接数和圆二色性测量了陈恩数。此外，该团队还介绍了使用机器学习技术来改进拓扑相变的识别。在第二个资助期，汉堡项目将以这些技术为基础，并将研究在弱相互作用和强相互作用体系中拓扑和相互作用的丰富相互作用。我们将制备和表征波色子和费米子在拓扑带结构中的多体相，包括平衡态和猝灭后的动力学态。我们将实现一个六边形超晶格，这对于制备分数填充至关重要，但也允许在驱动光学Kagome晶格中研究拓扑三带模型。此外，我们将实现准无序，并研究与拓扑和相互作用的相互作用，期望观察拓扑对无序和二维拓扑安德森绝缘子的保护。汉堡项目将与研究单位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方案。

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.