Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array

Topological and strongly correlated materials are exciting frontiers in condensed-matter physics, married prominently in studies of the fractional quantum Hall effect [H.L. Stormer et al., Rev. Mod. Phys. 71, S298 (1999)], There is an active effort to develop synthetic materials where the microscopic dynamics and ordering arising from the interplay of topology and interaction may be directly explored. In this work, we demonstrate an architecture for exploration of topological matter constructed from tunnel-coupled, time-reversal-broken microwave cavities that are both low loss and compatible with Josephson-junction-mediated interactions [A. Wallraff et al., Nature (London) 431, 162 (2004)]. Following our proposed protocol [B.M. Anderson et al., Phys. Rev. X 6, 041043 (2016)], we implement a square lattice Hofstadter model at a quarter flux per plaquette (alpha = 1/4), with time-reversal symmetry broken through the chiral Wannier orbital of resonators coupled to yttrium-iron-garnet spheres. We demonstrate site-resolved spectroscopy of the lattice, time-resolved dynamics of its edge channels, and a direct measurement of the dispersion of the edge channels. Finally, we demonstrate the flexibility of the approach by erecting a tunnel barrier and investigating dynamics across it. With the introduction of Josephson junctions to mediate interactions between photons, this platform is poised to explore strongly correlated topological quantum science in a synthetic system.