Coordination Funds

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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.