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.
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