Band Engineering for Quantum Simulation in Circuit QED

The field of circuit QED has emerged as a rich platform for both quantum com- putation and quantum simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit. Combined with strong qubit-photon interactions, these systems can be used to study dynamical phase tran- sitions, many-body phenomena, and spin models in driven-dissipative systems. I will show that these waveguide cavities are uniquely deformable and can produce lattices and networks which cannot readily be obtained in other systems, including periodic lattices in a hyperbolic space of constant negative curvature. Furthermore, I will show that the one-dimensional nature of CPW resonators leads to degenerate flat bands and that criteria for when they are gapped can be derived from graph-theoretic techniques. The resulting gapped flat-band lattices are difficult to realize in standard atomic crys- tallography, but readily realizable in superconducting circuits.