  Cavity quantum electrodynamics, which explores the granularity of light by
coupling a resonator to a nonlinear emitter, has played a foundational role in
the development of modern quantum information science and technology. In
parallel, the field of condensed matter physics has been revolutionized by the
discovery of underlying topological robustness in the face of disorder, often
arising from the breaking of time-reversal symmetry, as in the case of the
quantum Hall effect. In this work, we explore for the first time cavity quantum
electrodynamics of a transmon qubit in the topological vacuum of a
Harper-Hofstadter topological lattice. To achieve this, we assemble a square
lattice of niobium superconducting resonators and break time-reversal symmetry
by introducing ferrimagnets before coupling the system to a single transmon
qubit. We spectroscopically resolve the individual bulk and edge modes of this
lattice, detect vacuum-stimulated Rabi oscillations between the excited
transmon and each mode, and thereby measure the synthetic-vacuum-induced Lamb
shift of the transmon. Finally, we demonstrate the ability to employ the
transmon to count individual photons within each mode of the topological band
structure. This work opens the field of chiral quantum optics experiment,
suggesting new routes to topological many-body physics and offering unique
approaches to backscatter-resilient quantum communication.
