Quantum Microwave Radiation and its Interference Characterized by Correlation Function Measurements in Circuit Quantum Electrodynamics

Superconducting circuits provide an attractive architecture for quantum optics experiments in solid state systems. Microwave radiation interacts strongly with individual (macroscopic) quantum systems, and enables to realize emitters of single photons. The statistical property of emitting exactly a single photon as information carrier makes these emitters relevant for quantum communication and information processing protocols. To display statistical properties of a radiation source, their correlation functions are usually measured. In the optical frequency domain this is realized using photo detectors. At microwave frequencies linear amplifiers effectively measure the amplitude of propagating electromagnetic fields. However, noise necessarily added to the microwave signal in the process of amplification and inefficiencies of correlation function measurements prevented studies of the statistics of microwave-frequency quantum fields and their interference effects up to now. In this thesis I discuss the statistical characterization of continuous and pulsed single-photon sources, and investigate two-photon interference at an on-chip beam splitter. I demonstrate that even in the presence of a high noise level characteristic for conventional microwave amplifiers, the photon statistics of quantum radiation sources can be acquired. Correlation functions are extracted by recording the linearly amplified electromagnetic field and analyzing it using efficient digital signal processing. Field programmable gate array (FPGA) based electronics is developed to process and average these data continuously and in real-time. Through first-order correlations I investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra. Single-photon antibunching is clearly observed in second-order correlation function measurements. We fully characterize the coalescence of indistinguishable single photons at an on-chip beam splitter into a pair of photons, generating non-local entanglement in the beam splitter output modes. The measurement device developed within this thesis project has widely broadened microwave frequency signal analysis, and enables real-time feed-back in future experiments due to customizable signal processing. The presented experiments constitute a first step towards using single-photon sources and two-photon interference at microwave frequencies for quantum communication and information processing.