Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum 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.

Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics and for studies on propagating quantum microwaves because of their good 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 9 These authors contributed equally to this work.

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 galvanically to the qubit. With a coupling strength as high as 17.5% 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 approximation. 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 frequency-degenerate superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux 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 controlling the qubit population via a microwave drive. Our measurements allow us to find parameter regimes for optimal coupler performance and quantify the tunability range.

Quantum state reconstruction involves measurement devices that are usually described by idealized models, but not known in full detail in experiments. For weak propagating microwaves, the detection process requires linear amplifiers which obscure the signal with random noise. Here, we introduce a theory which nevertheless allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross-correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves.

We use a correlation function analysis of the field quadratures to characterize both the black body radiation emitted by a 50 Ω load resistor and the quantum properties of two types of beam splitters in the microwave regime. To this end, we first study vacuum fluctuations as a function of frequency in a Planck spectroscopy experiment and then measure the covariance matrix of weak thermal states. Our results provide direct experimental evidence that vacuum fluctuations represent the fundamental minimum quantum noise added by a beam splitter to any given input signal.PACS numbers: 42.79. Fm,42.50.Lc, At optical frequencies, single-photon detectors [1] and beam splitters are key ingredients for the successful development of atomic physics and quantum optics. These devices are crucial for the implementation of quantum homodyne tomography [2], quantum information processing and communication [3], as well as all-optical quantum computing [4]. The recent advent of circuit quantum electrodynamics (QED) [5][6][7][8][9][10][11][12][13][14][15] has paved the way for the generation of single photons in the microwave (mw) regime [11,15]. Despite the rapid advances in this prospering field, the availability of suitable mw photodetectors [16,17] and well-characterized mw beam splitters is still at an early stage. However, we have recently shown that the use of low-noise cryogenic high electron mobility transistor (HEMT) amplifiers represents a versatile and powerful approach for the analysis of both classical and non-classical mw signals on a single photon level. Although the phase-insensitive HEMT amplifiers obscure the signal by adding random noise of typically 10-20 photons at 5 GHz, they do not perturb the correlations of signals opportunely split into two parts and then processed by two parallel amplification and detection chains. In such a setup, a correlation analysis allows for full state tomography of propagating quantum mw signals and the detector noise, simultaneously [18]. We note that HEMT amplifiers represent available "off-the-shelf" technology and offer flat gain over a broad frequency range of several GHz. Here, we present results of two experiments demonstrating the successful application of our setup to the characterization of weak thermal states. In a first experiment denoted as Planck spectroscopy we analyze the mw black body radiation emitted by a matched 50 Ω load resistor as a function of temperature in the frequency regime 4.7 ≤ ω/2π ≤ 7.1 GHz. Besides confirming that the mean thermal photon number follows Bose-Einstein statistics [19,20], our data directly show that the quantum crossover temperature T cr shifts with frequency as T cr = ω/2k B , providing an indirect measure of mw vacuum fluctuations with high fidelity. In a second experiment, we use weak thermal states for a detailed experimental characterization of mw beam splitters at the quantum level. This task, which has not been accomplished previously, is particularly important because mw beam splitters are key elements in a variety of quantumo...

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 inductance between the resonators. From the mode distance observed in spectroscopy experiments, we derive a coupling strength g/2π ranging between −320 MHz and 37 MHz. In the case of g ≈ 0 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.

A superconducting qubit coupled to an open transmission line represents an implementation of the spin-boson model with a broadband environment. We show that this environment can be engineered by introducing partial reflectors into the transmission line, allowing to shape the spectral function, J(ω), of the spin-boson model. The spectral function can be accessed by measuring the resonance fluorescence of the qubit, which provides information on both the engineered environment and the coupling between qubit and transmission line. The spectral function of a transmission line without partial reflectors is found to be Ohmic over a wide frequency range, whereas a peaked spectral density is found for the shaped environment. Our work lays the ground for future quantum simulations of other, more involved, impurity models with superconducting circuits.