Photonic topological boundary pumping as a probe of 4D quantum Hall physics

Topological light-trapping on a dislocation

Topological insulators have unconventional gapless edge states where disorder-induced back-scattering is suppressed. In photonics, such edge states lead to unidirectional waveguides which are useful for integrated photonic circuitry. Cavity modes, another type of fundamental component in photonic chips, however, are not protected by band topology because of their lower dimensions. Here we demonstrate that concurrent wavevector space and real-space topology, dubbed as dual-topology, can lead to light-trapping in lower dimensions. The resultant photonic-bound state emerges as a Jackiw-Rebbi soliton mode localized on a dislocation in a two-dimensional photonic crystal, as proposed theoretically and discovered experimentally. Such a strongly confined cavity mode is found to be robust against perturbations. Our study unveils a mechanism for topological light-trapping in lower dimensions, which is invaluable for fundamental physics and various applications in photonics.

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Exploring 4D quantum Hall physics with a 2D topological charge pump

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 effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. 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 number. 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 effect. 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 predicted.