Exploring 4D quantum Hall physics with a 2D topological charge pump
Jan 4, 2018Citations per year
Abstract: (Springer)
By implementing a 2D topological charge pump using ultracold bosonic atoms, the theoretically predicted 4D integer quantum Hall effect is confirmed experimentally. The quantum Hall effect, discovered in the 1980s, is an important fundamental effect in condensed matter physics that links topological states with electronic properties in two-dimensional systems. The quantized conductance is prescribed by an integer global topological invariant and is therefore protected against perturbations. Such invariants are characterized by a so-called Chern number. Two papers in this issue experimentally confirm the prediction that the quantum Hall effect can be generalized to a four-dimensional (4D) system. Immanuel Bloch and colleagues implement the 4D quantum Hall system in a superlattice of ultracold bosonic atoms, and Mikael Rechtsman and colleagues achieve the same in a photonic waveguide array. Both groups find that their system harbours a second Chern number, as expected. The studies show an intriguing advance towards new physics provided by topological protection in higher dimensions. The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect1: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field2. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number3,4. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect5,6. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted4.- Quantum Hall
- Quantum simulation
- Ultracold gases
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