Interacting Photons in Curved Space Using Superconducting Circuits

After close to two decades of research and development, superconducting circuits have emerged as a rich platform for both quantum computation and quantum simulation. In this talk, we will discuss a new domain of quantum simulation with superconducting circuits: interacting photons in curved (non-Euclidean) space. By constructing two-dimensional lattices of microwave coplanar waveguide cavities with spatially-varying hopping rates and resonant frequencies, we demonstrate that we can simulate photons propagating in non-Euclidean space. Furthermore, superconducting circuits allow us to engineer effective photon-photon interactions using high kinetic inductance nonlinearites and transmon qubits--introducing the exciting prospect of studying strongly-interacting photons in curved geometries.