Coordination Funds

拓扑学已经成为表征量子物质的一个重要概念，它与对称性一起产生了大量的新相和奇异相。在拓扑不同相之间的界面上，看似不可能的现象成为现实，如电荷分馏，手性电流或单狄拉克锥。因为拓扑现象产生了极其精确的量子化和对无序的鲁棒性，它们有望改变从计量到量子计算的游戏规则应用。拓扑效应是当前研究的热点，新概念和新拓扑材料正以惊人的速度被发现。拓扑和强相互作用的相互作用是凝聚态物理中最具活力和挑战性的问题之一。由于拓扑性质和相互作用不能在真实材料中独立调谐，拓扑系统的量子模拟器越来越受到关注。特别是，光学晶格中的超冷原子已经成为结合强人工规范场和具有可调谐强相互作用的拓扑带结构的多功能平台。由于原子是电荷中性的，所以规范场是通过激光耦合和使用强大的Floquet技术来设计的。实现了多种实验平台，实现了霍夫施塔特模型、霍尔丹模型、阶梯系统和一维链的研究。此外，无序格和准周期格也可以实现。除了固体效应的量子模拟，冷原子还允许研究更奇特的系统，如玻色子系统、高自旋系统或高维系统，因此，提供了没有任何静态对应物的四维量子霍尔效应或异常Floquet拓扑系统的访问。最后，将人工规范场与量子气体显微镜相结合，可以实现对拓扑系统的单点访问，并有望获得对强相关相的新见解，并直接操纵奇异激发。在第一个资助期内，该研究单位为这些发展做出了重大贡献，将冷原子研究推向了拓扑物理学的前沿。这是通过实验和理论的共同努力，使用最先进的实验、分析和数值技术实现的。在第二个资助期，重点将放在实现相互作用的拓扑相，并最终实现分数陈氏绝缘体。我们将提供必要的理论背景，并系统地研究拓扑状态的工程和制备。此外，我们将推动该领域达到新的极限，如非阿贝尔激励和动态规范场，这也为高能物理提供了一座桥梁。我们结合实验和理论的努力将导致对相互作用拓扑物质的重要见解，并为未来的应用铺平道路。

Topology has emerged as an important concept for characterizing quantum matter, which, together with symmetry, gives rise to a plethora of new and exotic phases. At the interface between topologically distinct phases, seemingly impossible phenomena become reality, such as charge fractionalization, chiral currents or single Dirac cones. Because topological phenomena give rise to extremely precise quantization and robustness against disorder, they hold promise for game-changing applications ranging from metrology to quantum computation. Topological effects are at the focus of current research, with new concepts and new topological materials being discovered at an amazing pace. The interplay of topology and strong interactions is one of the most vibrant and challenging problems in condensed-matter physics. Because topological properties and interactions cannot be tuned independently in real materials, quantum simulators of topological systems have gained increasing attention. In particular, ultracold atoms in optical lattices have emerged as a versatile platform for combining strong artificial gauge fields and topological band structures with tunable strong interactions. Because the atoms are charge-neutral, gauge fields are engineered by laser couplings and using powerful Floquet techniques. Diverse experimental platforms have been realized, enabling studies of the Hofstadter model, the Haldane model, ladder systems and one-dimensional chains. Moreover, disorder and quasiperiodic lattices can be implemented. Next to the quantum simulation of solid-state effects, cold atoms also allow to study even more exotic systems such as bosonic systems, highspin systems or high-dimensional systems, hence, providing access to the 4d quantum Hall effect or anomalous Floquet topological systems without any static counterpart. Finally, combining artificial gauge fields with quantum-gas microscopy allows single-site access to topological systems with the promise to gain new insights into strongly-correlated phases and to directly manipulate exotic excitations. In the first funding period, this Research Unit has significantly contributed to these developments, which bring cold atoms research to the forefront of topological physics. This was possible via a joint effort of experiment and theory using the most advanced experimental, analytical and numerical techniques. In the second funding period, the focus will be on realizing interacting topological phases and, ultimately, fractional Chern insulators. We will provide the necessary theoretical background and systematically study engineering and preparation of topological states. Furthermore, we will push the field to new limits such as non-abelian excitations and dynamical gauge fields, which also provide a bridge to high-energy physics. Our combined experimental and theoretical effort will lead to important insights into interacting topological matter and pave the way for future applications.