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The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example thereof is the two-dimensional integer quantum Hall effect. It is characterized by the first Chern number which manifests in the quantized Hall response induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional systems leads to the appearance of a novel non-linear Hall response that is quantized as well, but described by a 4D topological invariant - the second Chern number. Here, we report on the first observation of a bulk response with intrinsic 4D topology and the measurement of the associated second Chern number. By implementing a 2D topological charge pump with ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small atom cloud as a local probe, we fully characterize the non-linear response of the system by in-situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probe higher-dimensional quantum Hall systems, where new topological phases with exotic excitations are predicted.
Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally st
A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the wrong chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp co
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems,
We propose and analyze a general scheme to create chiral topological edge modes within the bulk of two-dimensional engineered quantum systems. Our method is based on the implementation of topological interfaces, designed within the bulk of the system
While ferromagnets have been known and exploited for millennia, antiferromagnets (AFMs) were only discovered in the 1930s. The elusive nature indicates AFMs unique properties: At large scale, due to the absence of global magnetization, AFMs may appea