Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics. To this end, the strong nonlinearitiesof superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain. In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task. In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach-Zehnder interferometer composed of two superconducting microwave beam splitters. By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment. At high frequencies, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit. At low frequencies, we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators. Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.

Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays animportant role in quantum teleportation protocols with continuous variables. In our experiments we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states stays constant over a wide range of the displacement power.

We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductancebetween the resonators. From the mode distance observed in spectroscopy experiments, we derive a coupling strength ranging between -320MHz and 37 MHz. In the case where the coupling strength is about zero, the microwave power cross transmission between the two resonators can be reduced by almost four orders of magnitude compared to the case where the coupling is switched on. In addition, we observe parametric amplification by applying a suitable additional drive tone.

Propagating quantum microwaves have been proposed and successfully implemented to generate entanglement, thereby establishing a promising platform for the realisation of a quantum communicationchannel. However, the implementation of quantum teleportation with photons in the microwave regime is still absent. At the same time, recent developments in the field show that this key protocol could be feasible with current technology, which would pave the way to boost the field of microwave quantum communication. Here, we discuss the feasibility of a possible implementation of microwave quantum teleportation in a realistic scenario with losses. Furthermore, we propose how to implement quantum repeaters in the microwave regime without using photodetection, a key prerequisite to achieve long distance entanglement distribution.

We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanicallyto the qubit. With a coupling strength as high as 17% of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings model. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.

We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent currentflux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit drive power and the dynamic range of the resonator input power

We study quantum state tomography, entanglement detection, and channel noise reconstruction of propagating quantum microwaves via dual-path methods. The presented schemes make use ofthe following key elements: propagation channels, beam splitters, linear amplifiers, and field quadrature detectors. Remarkably, our methods are tolerant to the ubiquitous noise added to the signals by phase-insensitive microwave amplifiers. Furthermore, we analyze our techniques with numerical examples and experimental data. Our methods provide key toolbox components that may pave the way towards quantum microwave teleportation and communication protocols.

Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics (QED) and for studies on propagating quantum microwaves because of theirgood noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis we apply dual-path cross-correlation techniques to reconstruct the Wigner functions of various squeezed vacuum and thermal states. At 10 dB signal gain, we find 4.9+-0.2 dB squeezing below vacuum. In addition, we discuss the physics behind squeezed coherent microwave fields. Finally, we analyze the JPA noise temperature in the degenerate mode and find a value smaller than the standard quantum limit for phase-insensitive amplifiers.

Path entanglement constitutes an essential resource in quantum information
and communication protocols. Here, we demonstrate frequency-degenerate
entanglement between continuous-variablequantum microwaves propagating along
two spatially separated paths. We combine a squeezed and a vacuum state using a
microwave beam splitter. Via correlation measurements, we detect and quantify
the path entanglement contained in the beam splitter output state. Our
experiments open the avenue to quantum teleportation, quantum communication, or
quantum radar with continuous variables at microwave frequencies.