The Circuit Quantum Electrodynamical Josephson Interferometer

Arrays of circuit cavities offer fascinating perspectives for exploring quantum many-body systems in a driven dissipative regime where excitation losses are continuously compensated by coherent input drives. Here we investigate a system consisting of three transmission line resonators, where the two outer ones are driven by coherent input sources and the central resonator interacts with a superconducting qubit. Whereas a low excitation number regime of such a device has been considered previously with a numerical integration, we here specifically address the high excitation density regime. We present analytical approximations to these regimes in the form of two methods. The first method is a Bogoliubov or linear expansion in quantum fluctuations which can be understood as an approximation for weak nonlinearities. As the second method we introduce a combination of mean-field decoupling for the photon tunneling with an exact approach to a driven Kerr nonlinearity which can be understood as an approximation for low tunneling rates. In contrast to the low excitation regime we find that for high excitation numbers the anti-bunching of output photons from the central cavity does not monotonously disappear as the tunnel coupling between the resonators is increased.Comment: revised, comparison of numerics and mean-field adde

Hybrid Quantum Systems: Resonator State Preparation with Rydberg Atom Beams

In this thesis theoretical studies of hybrid quantum systems composed of solid-state superconducting microwave resonators, mechanical oscillators, and gas-phase Rydberg atoms are described. The thesis begins with an overview of the current state of the field of hybrid quantum in- formation processing. An introduction to the physics of Rydberg atoms and the preparation processes of circular Rydberg states follows, including a review of the associated literature. Three main new research results are then presented. These include (1) numerical studies of static electric dipole interactions in strongly polarized gases of Rydberg atoms. The understanding and characterization of these interactions is essential to maximize the quantum-state preparation procedures required for the hybrid systems studied in the thesis; (2) analytical and numerical studies of quantum-state preparation and cooling in coplanar superconducting microwave resonators using beams of atoms in circular Rydberg states; and (3) studies of coupled Rydberg-atom—mechanical-oscillator systems. The results presented in each of these areas are of interest for hybrid quantum information processing and quantum computation, and optical-to- microwave photon conversion for quantum communication