Topological Effects in Low-dimensional Quantum Gases

拓扑概念在物理现象的描述中越来越重要。凝聚态物理学中的突出例子包括量子霍尔效应和拓扑绝缘体的迷人电子特性。在相互作用的存在下，具有更有趣的电子性质的多体状态已经被预测，它们表现出分数电荷的激发和非平凡的统计，既不是玻色子也不是费米子。光学晶格中超冷原子的量子模拟为研究这些非平凡拓扑多体系统提供了一条很有前途的途径。实验已经取得了令人印象深刻的结果的工程和表征的拓扑能带结构。然而，到目前为止，这些研究大多局限于非相互作用的制度。将实验协议扩展到相互作用机制需要理论和实验的共同努力。在这个研究单位，我们追求以下两个主要目标：低熵分数陈省身绝缘体的制备和实验观测的发展，研究拓扑多体状态的奇异特性。为了实现这些具有挑战性的目标，我们采用以下策略：（i）继续进行实验努力，实现长寿命的拓扑系统中的弱相互作用制度，这已被发现是有限的相互作用引起的，以及技术加热。在此背景下，我们还将致力于生成静态系统中没有类似物的新型拓扑系统，研究拓扑与无序之间的相互作用，研究双层系统中的拓扑邻近效应，并开发替代实验技术来实现拓扑系统。(ii)设计和建造一个量子气体显微镜，这将提供新的实验观测和技术，通过本地观测和接口准备和研究拓扑多体系统。此外，我们将与该研究单元的理论团队合作，以确定适合直接研究任意子模型的光学晶格设置，并扩展当前平台以研究动态规范场。

Topological concepts have gained increasing importance in the description of physical phenomena. Prominent examples in condensed matter physics include the quantum Hall effect and the fascinating electronic properties of topological insulators. In the presence of interactions, many-body states with even more intriguing electronic properties have been predicted, which exhibit excitations with fractional charges and non-trivial statistics that are neither bosonic nor fermionic. Quantum simulations with ultracold atoms in optical lattices constitute a promising avenue for studying these non-trivial topological many-body systems. Experiments have achieved impressive results on the engineering and characterization of topological band structures. However, so far these studies were mostly limited to the non-interacting regime. Extending the experimental protocols to the interacting regime requires the combined effort of theory and experiments. Within this Research Unit we pursue the following two main goals: the preparation of low-entropy fractional Chern insulators and the development of experimental observables to study the exotic properties of topological many-body states. In order to achieve these challenging goals, we employ the following strategy: (i) Continue ongoing experimental efforts for realizing long-lived topological systems in the weakly-interacting regime, which have been found to be limited by interaction-induced as well as technical heating. In this context we will also work towards generating novel topological systems, which have no analog in static systems, study the interplay between topology and disorder, investigate topological proximity effects in bilayer systems and develop alternative experimental techniques to realize topological systems. (ii) Design and construct a quantum gas microscope, which will provide access to novel experimental observables and techniques for preparing and studying topological many-body systems via local observables and interfaces. Moreover, we will collaborate with the theory teams of this Research Unit in order to identify optical lattice settings that are suited to directly study anyonic models and extend current platforms to investigate dynamical gauge fields.