Cavity QED in a Synthetic Gauge Field

Recent advances in the ability to fabricate and manipulate superconducting quantum circuits have opened up exciting opportunities to construct from the ground up synthetic quantum materials hosting rich interactions. We have designed a cavity QED system which harnesses strong interactions between a highly nonlinear transmon qubit and a quarter-flux Hofstadter lattice realized for microwave photons. In this system, a single transmon qubit couples to a 2D lattice of high-Q microwave resonators which interact strongly with magnetic-field-biased ferrimagnets, producing a synthetic magnetic field for photons and giving rise to a topological bandstructure that hosts chiral edge channels. We demonstrate chiral, time-reversal-symmetry-broken edge transport in this lattice with excitation lifetimes exceeding ~1000 times the site-to-site tunneling rate. We also demonstrate strong interactions between the chiral lattice and transmon qubit, measuring Rabi swapping of excitations from the transmon qubit to a range of lattice eigenmodes on timescales ~10 times faster than lattice excitation decay times. We non-destructively measure photon occupation of lattice eigenmodes by characterizing number splitting of dispersive shifts in the qubit transition. Finally, we describe work towards coupling multiple transmon qubits to the chiral lattice edge, enabling quantum communication via edge channels, supporting exploration of photon-photon interactions in a topological bandstructure, and opening avenues towards investigating many-body physics in this synthetic material.