Cavity quantum electrodynamics, which explores the granularity of light by coupling a resonator to a nonlinear emitter¹, 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^2,3,4, often arising from the breaking of time-reversal symmetry, as in the case of the quantum Hall effect. In this work, we explore the cavity quantum electrodynamics of a transmon qubit in a topologically nontrivial Harper–Hofstadter lattice⁵. We assemble the lattice of niobium superconducting resonators⁶ and break time-reversal symmetry by introducing ferrimagnets⁷ before coupling the system to a transmon qubit. We spectroscopically resolve the individual bulk and edge modes of the lattice, detect Rabi oscillations between the excited transmon and each mode and measure the synthetic-vacuum-induced Lamb shift of the transmon. Finally, we demonstrate the ability to employ the transmon to count individual photons⁸ within each mode of the topological band structure. This work opens the field of experimental chiral quantum optics⁹, enabling topological many-body physics with microwave photons ^10,11 and providing a route to backscatter-resilient quantum communication.

^{腔量子电动力学通过将谐振器耦合到非线性发射器1}来探索光的粒度，在现代量子信息科学技术的发展中发挥了基础性作用。与此同时，凝聚态物理领域因发现底层拓扑^2,3,4而发生了革命性变化，这通常是由于时间反转对称性的破坏而引起的，例如量子霍尔效应。^{在这项工作中，我们在拓扑非平凡的 Harper-Hofstadter 晶格5}中探索了 transmon 量子比特的腔量子电动力学。我们组装了铌超导谐振器⁶的晶格，并通过引入铁磁体^{7打破了时间反演对称性}在将系统耦合到 transmon qubit 之前。我们通过光谱解析晶格的单个体模和边缘模，检测激发的 transmon 和每个模式之间的 Rabi 振荡，并测量 transmon 的合成真空诱导的 Lamb 位移。最后，我们展示了使用 transmon在拓扑能带结构的每个模式中计算单个光子^{8的能力。}这项工作开辟了实验手性量子光学⁹的领域，使拓扑多体物理与微波光子^10,11成为可能，并提供了反向散射弹性量子通信的途径。