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

## TL;DR

This paper demonstrates the first experimental observation of a 4D quantum Hall effect using a 2D topological charge pump with ultracold atoms, revealing a non-linear, quantized response linked to a 4D topological invariant.

## Contribution

It introduces a method to realize and measure a 4D quantum Hall effect in a 2D system, enabling exploration of higher-dimensional topological phases.

## Key findings

- First measurement of a bulk 4D topological response
- Implementation of a dynamical 4D quantum Hall system
- Full characterization of non-linear topological response

## 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.