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.

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• Non-Abelian Anyons and Topological Quantum Computation
• Topological Photonics
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• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Coherent collisional spin dynamics in optical lattices

Cited by in corpus (7)

• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Realization of an acoustic third-order topological insulator
• Experimental band structure spectroscopy along a synthetic dimension
• Probing Weyl Physics with One-dimensional Sonic Crystals
• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• Sensing electrons during an adiabatic coherent transport passage
• Topologically protected quantization of work