. 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 a novel architecture for exploration of topological matter constructed from tunnel-coupled, time-reversalbroken microwave cavities that are both low loss and compatible with Josephson junction-mediated interactions [2]. Following our proposed protocol [3] 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 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 for the first time in a synthetic system.
Hamiltonian Tomography of Photonic Lattices
In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy
effective Hamiltonian between sites i and j may be obtained directly from Sij(ω), the (suitably normalized) two-port measurement between sites i and j at frequency ω. This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is actually a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band-projectors in finite, disordered systems with good flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in-between.