Topological Effects in Low-dimensional Quantum Gases

拓扑学概念在描述物理现象方面变得越来越重要。凝聚态物理中的突出例子包括量子霍尔效应和拓扑绝缘体的迷人的电子性质。在存在相互作用的情况下，预测了具有更有趣的电子性质的多体状态，这些状态显示出具有分数电荷的激发和非平凡的统计既不是玻色态也不是费米子的。光学晶格中超冷原子的量子模拟为研究这些非平凡的拓扑多体系统提供了一条很有前途的途径。实验在拓扑带结构的工程设计和表征方面取得了令人印象深刻的结果。然而，到目前为止，这些研究大多局限于非互动机制。将实验协议扩展到交互机制需要理论和实验的共同努力。在这个研究单位内，我们追求以下两个主要目标：制备低熵分数的陈氏绝缘体和发展实验观测，以研究拓扑多体状态的奇异性质。为了实现这些具有挑战性的目标，我们采用了以下策略：(I)继续正在进行的实验工作，以实现弱相互作用区域中的长寿命拓扑系统，这些系统已被发现受到相互作用诱导和技术加热的限制。在此背景下，我们还将致力于生成静态系统中没有模拟的新型拓扑系统，研究拓扑和无序之间的相互作用，研究双层系统中的拓扑邻近效应，并开发替代的实验技术来实现拓扑系统。(2)设计和建造量子气体显微镜，它将提供通过局部观察物和界面获得用于制备和研究拓扑多体系统的新的实验观察物和技术的途径。此外，我们将与这个研究单位的理论团队合作，以确定适合直接研究任意子模型的光学晶格设置，并扩展现有的平台来研究动态规范场。

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.