Exploring the topology of a quantum Hall system at the microscopic level.

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, and restrict the existence of fragile topological phases to defect-free samples. Artificial systems, as realized with photonic platforms or cold atomic gases, open novel possibilities by enabling specific probes of topology or flexible manipulation e.g. using synthetic dimensions encoded in internal degrees of freedom. However, the sizes of synthetic dimensions realized so far remain moderate, making the notion of a bulk irrelevant. Here, we realize a %disorder-free 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, $2J+1=17$, of magnetic sublevels leads to distinct behaviors in the bulk, where motion is inhibited due to a flattened energy band, and along the edges, where the particles are free to move in only one direction. We also show that the low-energy excitations take the form of cyclotron and skipping orbits. Furthermore, we measure the transverse drift induced by a weak force, and find a uniform Hall response in the bulk, reaching 98(5)% of the quantized value expected for a topological system. Our findings pave the way towards the realization of quantum many-body systems with non-trivial topology, such as mean-field Abrikosov vortex lattices or fractional quantum Hall states, as supported by numerical simulations of interacting bosons in our setting.