Hyperbolic and Flat-Band Lattices in Circuit QED
Abstract: After close to two decades of research and development, superconducting circuits have emerged as a rich platform for both quantum computation and quantum simulation. Lattices of superconducting coplanar waveguide (CPW) resonators have been shown to produce artificial materials for microwave photons, where weak interactions can be introduced either via non-linear resonator materials and strong interactions via qubit-resonator coupling. The unique deformability of coplanar waveguide microwave resonators enables realization of artificial photonic materials which cannot be made from ordinary atomic or ionic systems. We will present two such examples. First, we will introduce a technique using networks of CPW resonators to create a new class of materials which constitute regular lattices in an effective hyperbolic space with constant negative curvature. We will show numerical simulations of hyperbolic analogs of the kagome lattice which show unusual densities of states with spectrally-isolated degenerate flat bands. We will also present an experimental realization of one of these lattices as a proof of principle and a first step towards on-chip quantum simulation of materials science and interacting particles in curved space. Second, we will present a novel Euclidean lattice, called the heptagon-pentagon-kagome (HPK) lattice, which displays a flat band with a particularly large gap. Because this flat band is spectrally isolated and dispersion-less, interactions will be the dominant energy scale, enabling the study of strongly correlated, many-body photon states.