Probing chiral edge dynamics and bulk topology of a synthetic Hall system

Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct connection to simple topological models. Artificial systems, such as photonic platforms or cold atomic gases, open novel possibilities by enabling specific probes of topology or flexible manipulation e.g. using synthetic dimensions. However, the relevance of topological properties requires the notion of a bulk, which was missing in previous works using synthetic dimensions of limited sizes. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension and one synthetic dimension encoded in the atomic spin $J=8$. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors. Furthermore, we measure the Hall drift and reconstruct the local Chern marker, an observable that has remained, so far, experimentally inaccessible. In the center of the synthetic dimension -- a bulk of 11 states out of 17 -- the Chern marker reaches 98(5)% of the quantized value expected for a topological system. Our findings pave the way towards the realization of topological many-body phases.