Title: Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump,
Abstract: 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.