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 the frequency and time domains 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.

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 two different detection techniques. With the homodyne setup, we observe the 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 the 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.

Coupled superconducting transmission line resonators have applications in quantum information processing and fundamental quantum mechanics. A particular example is the realization of fast beam splitters, which however is hampered by two-mode squeezer terms. Here, we experimentally study superconducting microstrip resonators which are coupled over one third of their length. By varying the position of this coupling region we can tune the strength of the two-mode squeezer coupling from 2.4 5.44GHz. Nevertheless, the beam splitter coupling rate for maximally suppressed two-mode squeezing is 810MHz, enabling the construction of a fast and pure beam splitter.

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.

Superconducting qubits acting as artificial two-level atoms allow for controlled variation of the symmetry properties which govern the selection rules for single and multiphoton excitation. We spectroscopically analyze a superconducting qubit-resonator system in the strong coupling regime under one- and two-photon driving. Our results provide clear experimental evidence for the controlled transition from an operating point governed by dipolar selection rules to a regime where one- and two-photon excitations of the artificial atom coexist. We find that the vacuum coupling between qubit and resonator can be straightforwardly extracted from the two-photon spectra where the detuned two-photon drive does not populate the relevant resonator mode significantly.

We use a correlation function analysis of the field quadratures to characterize both the blackbody 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.

Quantum state reconstruction of weak propagating microwaves to date requires the use of linear amplifiers. We introduce a theory which, even in the presence of significant amplifier noise, 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.

Quantum state reconstruction involves measurement devices that are usually described by idealized models. However, in actual experiments, the properties of the measurement apparatus may not be understood in full detail. In the case of weak propagating microwaves, the detection process requires the use of amplifiers, which add random noise and are considered to be linear. Such setups have been proven to be sufficient for probing quantum systems, particularly in circuit quantum electrodynamics. Additionally, quantum states of propagating microwaves themselves can be valuable in quantum information processing and their full reconstruction represents an important open issue. Here, we first introduce a theory to measure all quadrature moments of propagating quantum microwaves using cross-correlations from a dual-path amplification setup. Moreover, the detector noise properties are determined simultaneously, allowing for detector tomography. Furthermore, we demonstrate the practical realization of our novel concept by proof-of-principle experiments with suitable classical mixtures of weak coherent microwaves.

Superconducting circuit quantum electrodynamics experiments with propagating microwaves require devices acting as beam splitters. Using niobium thin films on silicon and sapphire substrates, we fabricated superconducting 180{\deg} microstrip hybrid ring couplers, acting as beam splitters with center frequencies of about 6GHz. For the magnitude of the coupling and isolation we find -3.5+/-0.5dB and at least -15dB, respectively, in a bandwidth of 2GHz. We also investigate the effect of reflections at the superconductor-normal conductor contact by means of low temperature laser scanning microscopy. Our measurements show that our hybrid rings are well suited for on-chip applications in circuit quantum electrodynamics experiments.

Submitted for the MAR09 Meeting of The American Physical Society Cross-correlation heterodyne detection part II: Measuring microwave nontrivial propagating signals EDWIN P. MENZEL, MATTEO MARIANTONI, M. A. ARAQUE CABALLERO, F. DEPPE, E. HOFFMANN, T. NIEMCZYK, A. MARX, R. GROSS, Walther-Meissner-Institut and TU Muenchen, Garching, Germany, E. SOLANO, Departamento de Quimica Fisica, Universidad del Pais Vasco / Euskal Herriko Unibertsitatea, Bilbao, Spain — The accurate measurement of the first two moments of Gaussian states (e.g., coherent or squeezed states) allows for their complete characterization. This provides a tool to clarify the quantum nature of microwave radiation, an important issue for example in circuit quantum electrodynamics. We present a full experimental characterization of nontrivial microwave signals with an average photon number of the order of 1, whose variance exhibits an elaborate dependence on external control parameters. We experimentally access the entire covariance matrix by splitting the input signals via microwave beam splitters and performing cross-correlation measurements. In this manner, we are able to precisely resolve the first two moments, a challenging task at microwave frequencies. Furthermore, we succeeded to measure the third central moment of similar nontrivial signals. We acknowledge support from SFB631, NIM, EuroSQUIP, and the Ikerbasque Foundation. Edwin P. Menzel Walther-Meissner-Institut and TU Muenchen, Garching, Germany Date submitted: 21 Nov 2008 Electronic form version 1.4