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Cavity quantum electrodynamics, which explores the granularity of light by coupling a resonator to a nonlinear emitter [1], 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 [2-4], 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 [5]. To achieve this, we assemble a square lattice of niobium superconducting resonators [6] and break time-reversal symmetry by introducing ferrimagnets [7] before coupling the system to a single transmon qubit. We spectroscopically resolve the individual bulk and edge modes of this lattice, detect vacuumstimulated 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 [8] within each mode of the topological band structure. This work opens the field of chiral quantum optics experiment [9], suggesting new routes to topological many-body physics [10,11] and offering unique approaches to backscatter-resilient quantum communication.

We report the observation of a phase transformation which can occur in a microscopic double phase BSCCO whisker at room temperature. We performed electrical resistivity measurements by thermally cycling the whisker in the range 78-300 K in a helium atmosphere and observed a decrease of the Bi-2223 phase amount in favour of the Bi-2212 phase, accompanied by an increase in the T c of the Bi-2212 phase. A longer ageing of the whisker increased its resistance by about a factor of four at room temperature and caused a semiconducting behaviour at low temperature. We demonstrate that a simple electrical model can account for the experimental data and disentangle the contributions of the two phases.

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