Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured by using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.

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Phonons and their interactions with other phonons, electrons or photons drive energy gain, loss and transport in materials. Although the phonon density of states has been measured and calculated in bulk crystalline semiconductors, phonons remain poorly understood in nanomaterials, despite the increasing prevalence of bottom-up fabrication of semiconductors from nanomaterials and the integration of nanometre-sized components into devices. Here we quantify the phononic properties of bottom-up fabricated semiconductors as a function of crystallite size using inelastic neutron scattering measurements and ab initio molecular dynamics simulations. We show that, unlike in microcrystalline semiconductors, the phonon modes of semiconductors with nanocrystalline domains exhibit both reduced symmetry and low energy owing to mechanical softness at the surface of those domains. These properties become important when phonons couple to electrons in semiconductor devices. Although it was initially believed that the coupling between electrons and phonons is suppressed in nanocrystalline materials owing to the scarcity of electronic states and their large energy separation, it has since been shown that the electron-phonon coupling is large and allows high energy-dissipation rates exceeding one electronvolt per picosecond (refs 10-13). Despite detailed investigations into the role of phonons in exciton dynamics, leading to a variety of suggestions as to the origins of these fast transition rates and including attempts to numerically calculate them, fundamental questions surrounding electron-phonon interactions in nanomaterials remain unresolved. By combining the microscopic and thermodynamic theories of phonons and our findings on the phononic properties of nanomaterials, we are able to explain and then experimentally confirm the strong electron-phonon coupling and fast multi-phonon transition rates of charge carriers to trap states. This improved understanding of phonon processes permits the rational selection of nanomaterials, their surface treatments, and the design of devices incorporating them.

Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state.

Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasi-probability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.