Cooperative quantum phenomena in circuits with Josephson junctions: Strong driving, photon generation, and non-Gaussian noise

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A major trend in solid state physics has been the fabrication of integrated quantum circuits which allow for the implementation and observation of quantum phenomena with unprecedented accuracy. Particular progress has been achieved in tailoring superconducting devices and in coupling them to other quantum systems such as resonators or mesoscopic conductors. This opens the door to studying processes known in quantum optics as perturbative effects in so far unaccessible parameter regimes. Of crucial relevance for a quantitative understanding of these solid state devices is their embedding in complex environments, which necessitates theoretical tools beyond perturbative treatments. In this respect, a stochastic representation of the dynamics of open quantum systems provides the required efficiency, flexibility, and accuracy. The goals of this project are the development of corresponding numerical approaches for current and future devices containing Josephson junctions and, using these methods, the exploration of cooperative phenomena such as optimal control and cooling, inelastic charge transfer in superconducting circuits strongly correlated with photon distributions in resonators, and detection of non-Gaussian charge noise.