The violation of J. Bell's inequality with two entangled and spatially separated quantum twolevel systems (TLS) is often considered as the most prominent demonstration that nature does not obey "local realism". Under different but related assumptions of "macrorealism", plausible for macroscopic systems, Leggett and Garg derived a similar inequality for a single degree of freedom undergoing coherent oscillations and being measured at successive times. Such a "Bell's inequality in time", which should be violated by a quantum TLS, is tested here. In this work, the TLS is a superconducting quantum circuit whose Rabi oscillations are continuously driven while it is continuously and weakly measured. The time correlations present at the detector output agree with quantum-mechanical predictions and violate the inequality by 5 standard deviations.

The future development of quantum information using superconducting circuits requires Josephson qubits 1 with long coherence times combined with a high-fidelity readout. Significant progress in the control of coherence has recently been achieved using circuit quantum electrodynamics architectures 2,3 , where the qubit is embedded in a coplanar waveguide resonator, which both provides a well-controlled electromagnetic environment and serves as qubit readout. In particular, a new qubit design, the so-called transmon, yields reproducibly long coherence times 4,5 . However, a high-fidelity single-shot readout of the transmon, desirable for running simple quantum algorithms or measuring quantum correlations in multi-qubit experiments, is still lacking. Here, we demonstrate a new transmon circuit where the waveguide resonator is turned into a sample-and-hold detector-more specifically, a Josephson bifurcation amplifier 6,7 -which allows both fast measurement and single-shot discrimination of the qubit states. We report Rabi oscillations with a high visibility of 94%, together with dephasing and relaxation times longer than 0.5 µs. By carrying out two measurements in series, we also demonstrate that this new readout does not induce extra qubit relaxation.A common strategy to readout a qubit consists of coupling it dispersively to a resonator, so that the qubit states |0 and |1 shift the resonance frequency differently. This frequency change can be detected by measuring the phase of a microwave pulse reflected on (or transmitted through) the resonator. Such a method, successfully demonstrated with a Cooper pair box capacitively coupled to a coplanar waveguide resonator 2,3 (CPWR), faces two related difficulties that have so far prevented measurement of the qubit state in a single readout pulse (so-called single-shot regime): the readout has to be completed in a time much shorter than the time T 1 in which the qubit relaxes from |1 to |0 , and with a power low enough to avoid spurious qubit transitions 8 . This issue can be solved by using a sample-and-hold detector consisting of a bistable hysteretic system in which the two states of the system are brought in correspondence with the two qubit states. Such a scheme has been implemented in various qubit readouts 9,10 . In our experiment, the bistable system is a Josephson bifurcation amplifier 6,7 (JBA) obtained by inserting a Josephson junction in the middle of the CPWR (see Fig. 1). When driven by a microwave signal of properly chosen frequency and power, this nonlinear resonator can bifurcate between two dynamical states B and B with different intra-cavity field amplitudes and reflected phases. To exploit the hysteretic character of this process, we carry out the readout in two steps (see inset in Fig. 1 the measuring power during a time t H long enough to determine this state with certainty.JBAs were used previously to readout quantronium 11-13 and flux qubits, obtaining for the latter fidelities up to 87% (ref. 14) with quantum non-demolition character 15 . Here, we ...

We have designed, fabricated and measured high-Q λ/2 coplanar waveguide microwave resonators whose resonance frequency is made tunable with magnetic field by inserting a DC-SQUID array (including 1 or 7 SQUIDs) inside. Their tunability range is 30% of the zero field frequency. Their quality factor reaches up to 3×104 . We present a model based on thermal fluctuations that accounts for the dependance of the quality factor with magnetic field.

Fully controlled coherent coupling of arbitrary harmonic oscillators is an important tool for processing quantum information 1 . Coupling between quantum harmonic oscillators has previously been demonstrated in several physical systems using a two-level system as a mediating element 2,3 . Direct interaction at the quantum level has only recently been realized by means of resonant coupling between trapped ions 4,5 . Here we implement a tunable direct coupling between the microwave harmonics of a superconducting resonator by means of parametric frequency conversion 6,7 . We accomplish this by coupling the mode currents of two harmonics through a superconducting quantum interference device (SQUID) and modulating its flux at the difference (∼7 GHz) of the harmonic frequencies. We deterministically prepare a single-photon Fock state 8 and coherently manipulate it between multiple modes, effectively controlling it in a superposition of two different 'colours'. This parametric interaction can be described as a beamsplitter-like operation that couples different frequency modes. As such, it could be used to implement linear optical quantum computing protocols 9,10 on-chip 11 . The ability to create and manipulate quantum number states in a linear resonator is an important task in cavity quantum electrodynamics (QED; ref. 1). Early theory 6,7 predicted that parametric frequency conversion could be a way to implement a tunable direct coupling between quantized modes of different energies. Classically, two harmonic oscillators coupled through a time-varying element, modulated at the difference of the resonator frequencies, will periodically exchange energy. At the quantum level, this can be used to swap the quantum states of two harmonic modes. In optics, the efficiency and quantum coherence of frequency up-conversion have been demonstrated using a pumped nonlinear crystal to couple light at different wavelengths [12][13][14] . However, in these experiments it is challenging to access the state dynamics because strong coupling rates are difficult to obtain 15 . In hybrid mechanical systems, strong parametric coupling, based on frequency conversion, has been recently achieved 16,17 , creating the possibility for the manipulation of quantum states of mesoscopic mechanical resonators 18 . In superconducting circuits, parametric processes have been used mainly to couple superconducting quantum bits (qubits) at their optimal points 19 , or to make quantum-limited microwave amplifiers [20][21][22][23] , yet little has been done with frequency conversion. Several circuit designs that enable frequency conversion between linear resonators have been proposed 21,24,25 . This particular interaction can be combined with the powerful tools already available in circuit QED (ref. dynamics of the parametric frequency conversion of a single photon between the first three internal resonant modes of a superconducting cavity, the state of which is prepared and read out with a superconducting qubit. Our circuit consists of a quarter-wave (λ/4) c...

We present the first experimental realization of a widely frequency tunable, nondegenerate three-wave mixing device for quantum signals at gigahertz frequency. It is based on a new superconducting building block consisting of a ring of four Josephson junctions shunted by a cross of four linear inductances. The phase configuration of the ring remains unique over a wide range of magnetic fluxes threading the loop. It is thus possible to vary the inductance of the ring with flux while retaining a strong, dissipation-free, and noiseless nonlinearity. The device has been operated in amplifier mode, and its noise performance has been evaluated by using the noise spectrum emitted by a voltage-biased tunnel junction at finite frequency as a test signal. The unprecedented accuracy with which the crossover between zero-point fluctuations and shot noise has been measured provides an upper bound for the noise and dissipation intrinsic to the device.

Time-dependent density functional theory faces an important problem when it comes to extended systems: The long-range component of the exchange-correlation kernel fxc is completely absent from local density or generalized gradient approximations, but it is believed to be present in the “exact” fxc. Several attempts have been made to solve this issue, the simplest of them being the use of a model static long-range kernel of the form −astatic /q2. In this paper, we propose and motivate a dynamical extension of this model of the form −(a+Bw2)/q2. The dynamical model is then used to calculate the dielectric function of a large variety of semiconductors and insulators. The absorption spectra of large gap insulators are remarkably improved with respect to calculations where the kernel is taken to be static. This approach is valid also for energies in the range of plasmons, and hence it yields, e.g., good electron energy loss spectra. Finally, we present some simple theoretical arguments that relate the parameters of the model to physical quantities, like the dielectric constant and the plasmon frequency

We report an experiment on the determination of the quantum nondemolition ͑QND͒ nature of a readout scheme of a quantum electrical circuit. The circuit is a superconducting quantum bit measured by microwave reflectometry using a Josephson bifurcation amplifier. We perform a series of two subsequent measurements, record their values and correlation, and quantify the QND character of this readout.

We have measured quantum interference between two single microwave photons trapped in the same superconducting resonator, whose frequencies are initially about 6 GHz apart. We accomplish this by use of a parametric frequency conversion process that mixes the mode currents of two cavity harmonics through a superconducting quantum interference device, and demonstrate that a two-photon entanglement operation can be performed with high fidelity.