In this work we show that a tunable coupling between microwave resonators can be engineered by means of simple Josephson junctions circuits, such as dc-and rf-SQUIDs. We show that by controlling the time dependence of the coupling it is possible to switch on and off and modulate the cross-talk, boost the interaction towards the ultrastrong regime, as well as to engineer red and blue sideband couplings, nonlinear photon hopping and classical gauge fields. We discuss how these dynamically tunable superconducting circuits enable key applications in the fields of all optical quantum computing, continuous variable quantum information and quantum simulation -all within the reach of state of the art in circuit-QED experiments.

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.

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.

Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an important 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 remains constant over a wide range of the displacement power.

In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n 2 + n photon number variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers 0.05 n 1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.As propagating electromagnetic fields in general [1][2][3], propagating microwaves with photon numbers on the order of unity are essential for quantum computation [4,5], communication [6], and illumination [7][8][9][10] protocols. Because of their omnipresence in experimental setups, the characterization of thermal states is especially relevant for many applications [11][12][13][14]. Specifically in the microwave regime, sophisticated experimental techniques for their generation at cryogenic temperatures, their manipulation, and detection have been developed in recent years. In this context, an important aspect is the generation of propagating thermal microwaves using thermal emitters [15][16][17]. These emitters can be spatially separated from the setup components used for manipulation and detection [18,19], which allows one to individually control the emitter and the setup temperature. Due to the low energy of microwave photons, the detection of these fields typically requires the use of nearquantum-limited amplifiers [20][21][22][23], cross-correlation detectors [17, 18, 24], or superconducting qubits [25][26][27][28].The unique nature of propagating fields is reflected in their photon statistics, which is described by a probability distribution either in terms of the number states or in terms of its moments. The former were studied by coupling the field to an atom or qubit and measuring the coherent dynamics [29][30][31] or by spectroscopic analysis [32]. The moment-based approach requires knowledge on the average photon number n and its variance Var(n) = n 2 − n 2 to distinguish many states of interest. To this end, the second-order correlation function g (2) (τ ) has been measured to analyze the photon statistics of thermal [33][34][35] or quantum [36][37][38] emitters ever since the ground-breaking experiments of Hanbury Brown and Twiss [39,40]. While these experiments use the time delay τ as control parameter, at microwave frequencies the photon number n can be controlled conveniently [15,32,[41][42][43][44]. In the specific case of a thermal field at frequency ω, the Bose-Einstein distribution yields n(T ) = [exp( ω/k B T ) − 1] −1 and Var(n) = n 2 + n, which can be controlled by the temperature T of the emitter. In practice, one wants to distinguish this relation from both the classical limit Var(n) = n 2 and the Poissonian behavior Var(n) = n characteristic for coherent states [41] or shot noise [45,46]. Hence, as shown in Fig. 1, the most relev...

We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. In particular, we investigate losses introduced by Nb/Al interfaces in the center conductor, which is important for experiments where Al based Josephson junctions are integrated into Nb based circuits. We find that these interfaces can be a strong source for twolevel state (TLS) losses, when the interfaces are not positioned at current nodes of the resonator. In addition to TLS losses, for resonators including Al, quasiparticle losses become relevant above 200 mK. Finally, we investigate how losses generated by eddy currents in conductive material on the backside of the substrate can be minimized by using thick enough substrates or metals with high conductivity on the substrate backside.

Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), which provide the JPA nonlinearity, for a finite screening parameter βL > 0 and demonstrate excellent agreement between the numerical results and the experimental data. Furthermore, we study the nondegenerate response of different JPAs and accurately describe the experimental results with our theory.