Quantum Nonlinearities in Strong Coupling Circuit QED

Circuit QED offers the possibility to realizean exceptionally strong coupling between artificial atoms - individual superconductingqubits - and single microwave photons in a one dimensional waveguide resonator. Thisnew solid state approach to investigate the matter-light interaction on the level of individual quanta also represents a promising hardware architecture for the realization of a scalable quantum information processor. We first summarize and review the important theoretical and experimental principles of this rapidely developing field and give an overview of the relevant literature. Here the focus is to provide a detailed discussion of the experimental ultra-low temperature measurement setup and the design, fabrication and characterization of superconducting Josephson junction devices. Presented key experimental results include: 1) The first clear observation of the Jaynes-Cummings nonlinearity in the vacuum Rabi spectrum by measuring both two- and three-photon dressed states. 2) The observation of strong collective coupling for up to 3 qubits. 3) A quantitative investigation of the quantum to classical transition induced by an elevated temperature environment.