Photons in Networks of Superconducting Circuits

Light consists of photons, mass-less particles that do not interact with one another in vacuum. Recent technological developments in superconducting circuits however enable us to engineer appreciable interactions between individual microwave photons in multiple nodes of a network simultaneously. In this talk, I will present some of our recent investigations for such devices.
On the one hand, strong photon-photon interactions can be employed to logically process information that is carried by the photons. Here I will discuss a scheme for a single photon transistor. On the other hand, such interactions allow us to drive photons into novel strongly correlated quantum many-body regimes. Interestingly, these may by studied in non-equilibrium scenarios where inevitable photon losses are constantly compensated by input drives. They thus give rise to an intriguing class of quantum many-body systems where instead of ground or thermal states one is interested in the still largely unexplored stationary states of their driven and dissipative dynamics. Here I will present some of our recent results for the phase diagrams for their stationary states.