Circuit QED Lattices in Hyperbolic Space

The field of circuit QED has seen dramatic progress in the field of quantum simu- lation with one of the exciting applications being the simulation of artificial materials for microwave photons. However, the physics of lattices of CPW resonators is purely determined by the connectivity of the resonators. This means that it is possible to construct networks of resonators which cannot be made from ordinary materials. We present one such example where we fabricate a two-dimensional periodic lattice in a hyperbolic space of constant negative curvature. This lattice constitutes an artificial material which exists in a fictitious very high gravitational field, and particles in the lattice propagate along geodesics of the hyperbolic metric, rather than along the standard straight lines of flat Euclidean space. Incorporating high-kinetic-inductance materials or transmon qubits will pave the way to table-top simulation of interacting and quantum mechanical particles in strong gravity.