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The discovery of topological states of matter has profoundly augmented ourunderstanding of phase transitions in physical systems. Instead of local orderparameters, topological phases are described by global topological invariantsand are therefore robust against perturbations. A prominent example thereof isthe two-dimensional integer quantum Hall effect. It is characterized by thefirst Chern number which manifests in the quantized Hall response induced by anexternal electric field. Generalizing the quantum Hall effect tofour-dimensional systems leads to the appearance of a novel non-linear Hallresponse 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 bulkresponse with intrinsic 4D topology and the measurement of the associatedsecond Chern number. By implementing a 2D topological charge pump withultracold bosonic atoms in an angled optical superlattice, we realize adynamical version of the 4D integer quantum Hall effect. Using a small atomcloud as a local probe, we fully characterize the non-linear response of thesystem by in-situ imaging and site-resolved band mapping. Our findings pave theway to experimentally probe higher-dimensional quantum Hall systems, where newtopological phases with exotic excitations are predicted.

Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump