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A long-lived multi-mode qubit register is an enabling technology for modular quantum computing architectures. For interfacing with superconducting qubits, such a quantum memory should be able to store incoming quantum microwave fields at the single-photon level for long periods of time, and retrieve them on-demand. Here, we demonstrate the partial absorption of a train of weak microwave fields in an ensemble of bismuth donor spins in silicon, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. The long storage time is obtained by biasing the bismuth donors at a clock transition. Phase coherence and quantum statistics are preserved in the storage., 11 pages including Supplementary

This corrects the article DOI: 10.1103/PhysRevLett.114.126801.

International audience; We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and intercorrelations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This nonclassical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.

We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear $I(V)$ curve. We also demonstrate that all quantities measured under a coherent time dependent bias can be reconstructed from their dc counterpart with a photo-assisted tunneling relation. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance and its current noise at the frequency of the resonator., Comment: Publisehd as Physical Review Letters, 114, 126801

We investigate the electronic transport properties of gold point contacts with superconducting aluminum leads. The modifications induced by the proximity effect in the quasiparticle density of states at the contact region are measured by tunnel spectroscopy. The theory of transport through multiple Andreev reflections is extended to incorporate these effects and used to determine the number and transmission coefficients of the conduction channels in the contact regime. We find that the smallest contacts, formed by one gold atom between the electrodes, contribute one single channel to the transport with variable transmission $T$ between 0.1 and 1.

We have measured the supercurrent in aluminum atomic point contacts containing a small number of well characterized conduction channels. For most contacts, the measured supercurrent is adequately described by the opposite contributions of two thermally populated Andreev bound states per conduction channel. However, for contacts containing an almost perfectly transmitted channel $0.9\ensuremath{\le}\ensuremath{\tau}\ensuremath{\le}1$ the measured supercurrent is higher than expected, a fact that we attribute to nonadiabatic transitions between bound states.

We have measured with a tunnel probe the energy distribution function of Landau quasiparticles in metallic diffusive wires connected to two reservoir electrodes, with an applied bias voltage. The distribution function in the middle of a 1.5-mm-long wire resembles the half sum of the Fermi distributions of the reservoirs. The distribution functions in 5- mm-long wires are more rounded, due to interactions between quasiparticles during the longer diffusion time across the wire. From the scaling of the data with the bias voltage, we find that the scattering rate between two quasiparticles varies as « 22 , where « is the energy transferred. [S0031-9007(97)04367-6] The present understanding of metals is based on Landau’s theory of Fermi liquids. In this model, the elementary excitations of the fluid of interacting electrons are nearly independent fermionic quasiparticles [1]. In disordered metals, residual interactions between quasiparticles lead in mesoscopic samples to measurable corrections to the density of states, and limit the phase coherence of quasiparticles [2]. These effects have been widely investigated experimentally and theoretically in the last 20 years [3]. However, the most elementary manifestation of interactions, namely, the transfer of energy between quasiparticles, has been observed only at energies of order 1 eV by time-resolved spectroscopy of a metallic film following a laser pulse [4], and in the meV range through the establishment of an electron temperature in the so-called hotelectron regime [5]. Indications as to the speed at which this thermalization proceeds were obtained in recent shot noise experiments [6]. In this Letter, we report a direct measurement of the energy transfer rates between quasiparticles in diffusive metallic wires. We have measured the energy distribution function of quasiparticles in wires in a stationary out-ofequilibrium situation, at low enough temperature so that quasiparticle-quasiparticle interaction is the dominant inelastic process. The deviations of the energy distribution function from the Fermi distribution give access to the energy transfer rates. We force the wire out of equilibrium by placing it between two reservoir electrodes [7] biased at different potentials, 0 and U, as shown in Fig. 1. The local distribution function is probed with a superconducting electrode connected to the wire by a tunnel junction. The experiment exploits the property of the distribution function to have different shapes depending on the amount of inelastic collisions a quasiparticle experiences during its diffusion time through the wire. The steady-state distribution function fsx, Ed in a metallic wire of length L, which depends on the position X › xL measured from the right electrode, and on the energy E, results from the combined action of the elastic diffusion and of interactions. It obeys the Boltzmann

We have investigated the suppression of single-electron charging effects in metallic single-electron transistors when the conductance of the tunnel junctions becomes larger than the conductance quantum ${e}^{2}/h$. We find that the Coulomb blockade of the conductance is progressively shifted at lower temperatures. The experimental results agree quantitatively with the available $1/T$ expansion at high temperature, and qualitatively with the predictions of an effective two-state model at low temperature, which predicts at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ a blockade of conductance for all gate voltages.

The isV , td curves present a series of sharp current steps at voltage values V › 2Dyne, where n is a positive integer and D is the superconducting gap. The well-known process of single quasiparticle transport corresponds to n › 1. The common phenomenon behind the other steps is multiple Andreev reflection (MAR) of quasiparticles between the two superconducting banks [14]. The order n › 2, 3, . . . , of a step corresponds to the number of electronic charges transferred in the underlying MAR process. As the transmission of the channel rises from 0 to 1, the higher order processes grow stronger and the subgap current increases progressively. This so-called “subharmonic gap structure” has already been observed in superconducting weak links and tunnel junctions with a very large number of channels [15,16]. Measurements [17] of the current-voltage characteristic ( IV ) of Nb and Pb single channel tunnel junctions with an adjustable transmission t1 have shown that the height of the successive current steps is proportional to increasing powers of t1 ,i n FIG. 1. Measured current-voltage characteristics (symbols) of four different configurations of sample #1 at 30 mK and best numerical fits (lines). The individual channel transmissions and total transmission T obtained from the fits are (a) t1 › 0.997, t2 › 0.46, t3 › 0.29, T › 1.747; (b) t1 › 0.74, t2 › 0.11, T › 0.85; (c) t1 › 0.46, t2 › 0.35, t3 › 0.07, T › 0.88; and (d) T › t1 › 0.025. Voltage and current are in reduced units. The measured superconducting gap was Dye › 182.5 6 2.0 mV. Left inset: Theoretical IVs for a single channel superconducting contact for different values of its transmission coefficient t (from bottom to top: 0.1, 0.4, 0.7, 0.9, 0.99, 1) after [12]. Right inset: Typical total transmission traces measured at V $ 5 Dye, while opening the contact at around 6 pmys, for samples #1 and #2. The bar indicates the distance scale.

An unshunted Josephson tunnel junction switching out of its zero-voltage state is a model system for thermal activation out of a metastable state. For small-capacitance low-critical-current junctions, this thermal activation process follows a generalized Arrhenius law involving dissipation directly in its exponent. This escape over a dissipation barrier can be computed exactly for a junction connected to a {ital RC} impedance providing large damping. The diffusion branch and the switching histograms measured for such a junction are in agreement with theory. {copyright} {ital 1996 The American Physical Society.}

We measure the quantum fluctuations of a pumped nonlinear resonator using a superconducting artificial atom as an in situ probe. The qubit excitation spectrum gives access to the frequency and amount of excitation of the intracavity field fluctuations, from which we infer its effective temperature. These quantities are found to be in agreement with theoretical predictions; in particular, we experimentally observe the phenomenon of quantum heating.

We have measured the current-voltage characteristic of a small capacitance tunnel junction coupled to a transmission line resonator. We calibrate the resonator using the sharp resonances displayed by the junction in the superconducting state, which corresponds to the pumping of the modes of the resonator by the ac Josephson current. With this calibration, we explain quantitatively the nonlinearity of the junction characteristic in the normal state as being due to the process by which a single electron tunnels by emitting a photon, the basic process of the theory of the effect of the electromagnetic environment on tunneling.

We have measured the supercurrent branch of a superconducting single electron transistor as a function of gate charge, temperature, and magnetic field. At low temperature and magnetic field, the switching current goes from a minimum to a maximum when the gate charge is varied from 0 to e, as expected for an island in the ground state with an even electron number. When the odd electron number ground state becomes populated by an increase of temperature or field, the Josephson tunneling is strongly suppressed, in agreement with theoretical predictions.

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. These results constitute a first proof of concept of spin-ensemble based quantum memory for superconducting qubits., 13 pages, 4 figures, plus supplementary information

We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own non-destructive single-shot readout. The fixed capacitive coupling yields the \sqrt{iSWAP} two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.

The dynamical Coulomb blockade (DCB) of tunneling is a quantum phenomenon in which tunneling of charge through a small tunnel junction is modified by its electromagnetic environment [1‐4]. This environment is described as an impedance in series with the tunnel element [see Fig. 1(a)]. The sudden charge transfer associated with tunneling can generate photons in the electromagnetic modes of the environment. In a normal metal tunnel junction, biased at voltage V, the energy eV of a tunneling electron can be dissipated both into quasiparticle excitations in the electrodes and into photons. At low temperature energy conservation forbids tunneling processes emitting photons with total energy higher than eV. This suppression reduces the conductance at low bias voltage [1,2,4]. In a Josephson junction, DCB effects are more prominent since at bias voltages smaller than the gap voltage 2� =e quasiparticle excitations cannot take away energy. Therefore, as sketched in Fig. 1(a), the entire energy 2eV of tunneling Cooper pairs has to be transformed into photons in the impedance for a dc current to flow through the junction [3,4]. Experiments have confirmed the predictions of DCB theory for the tunneling current, both in the normal [5‐7] and superconducting case [8,9] but the associated emission of photons into the environment has never been investigated. The aim of this work is to fill this gap by exploring the photonic side of DCB. We do so by embedding a Josephson junction into a well controlled electromagnetic environment provided by a microwave resonator. The resonator in turn leaks photons into an amplifier, allowing us to measure the rate and spectrum of photons emitted by the junction.

We have observed that the supercurrent across phase-biased, highly transmitting atomic size contacts is strongly reduced within a broad phase interval around {\pi}. We attribute this effect to quasiparticle trapping in one of the discrete sub-gap Andreev bound states formed at the contact. Trapping occurs essentially when the Andreev energy is smaller than half the superconducting gap {\Delta}, a situation in which the lifetime of trapped quasiparticles is found to exceed 100 \mus. The origin of this sharp energy threshold is presently not understood., Comment: Article (5 pages) AND Supplemental material (14 pages). To be published in Physical Review Letters

The basic current-carrying mechanism through a superconducting weak link embedded in a resistive environment undergoes a continuous crossover, as the voltage increases, from Josephson Cooper pair transfer exciting electromagnetic modes in the environment to multiple Andreev reflections leading to the creation of quasiparticles. We corroborate these ideas through measurements of the dc current-voltage characteristics of superconducting atomic contacts containing channels of arbitrary and adjustable transmission. We present a simple model, in the spirit of the classical resistively shunted junction model, that accounts well for the observed characteristics.

In order to probe quantitatively the effect of Kondo impurities on energy exchange between electrons in metals, we have compared measurements on two silver wires with dilute magnetic impurities (manganese) introduced in one of them. The measurement of the temperature dependence of the electron phase coherence time on the wires provides an independent determination of the impurity concentration. Quantitative agreement on the energy exchange rate is found with a theory by G\"{o}ppert et al. that accounts for Kondo scattering of electrons on spin-1/2 impurities., Comment: 4 pages

URL: http://www-spht.cea.fr/articles/s04/096; International audience; We have investigated the macroscopic quantum tunneling (MQT) of the phase across a Josephson junction embedded in a superconducting circuit. This system is equivalent to a spin 1/2 particle in a potential well. The MQT escape rate of such a particle was recently predicted to be strongly modified when a crossing of its inner Zeeman levels occurs while tunneling. In this regime, we observe a significant enhancement of the MQT rate and compare it to theory.

We have measured by tunneling spectroscopy the electronic density of states in a non-superconducting wire in good contact with a superconductor, at distances of 200, 300 and 800 nm from the interface. Closest to the interface, the density of states near the Fermi energy is reduced to 55% of its normal value. At the farthest measurement point, this dip has nearly completely disappeared. We compare our data to predictions based on the Usadel equations.

We have performed an interference experiment with two tunnel junctions between a thin normal metal wire and a superconducting fork. We have found that the subgap current is strongly modulated by the flux through the resulting normal-superconducting loop. Our results agree with the recent prediction that multiple tunnel attempts of electron pairs, which occur when electrons are confined near the junction, can add coherently if the pair consists of nearly time-reversed states.

We have measured the difference between the free energies of an isolated superconducting electrode with odd and even number of electrons using a Coulomb blockade electrometer. The decrease of this energy difference with increasing temperature is in good agreement with theoretical predictions assuming a BCS density of quasiparticle states, except at the lowest temperatures where the results indicate the presence of an extra energy level inside the gap.

The current-voltage characteristic of an ultrasmall tunnel junction is calculated for arbitrary frequency dependence of the impedance presented to the junction by its electromagnetic environment. It is shown that the Coulomb blockade of tunneling is washed out by quantum fluctuations of the charge on the junction capacitor except for ultrahigh impedance environments. Two simple cases where the environment can be treated as an inductor or resistor are examined in detail. Effects of finite temperatures are discussed.

The lifetime $\ensuremath{\tau}$ of the zero-voltage state of a current-biased Josephson junction in the thermal limit has been measured in the presence of a weak microwave perturbation. When the microwave frequency is close to the plasma frequency of the junction, the junction is "resonantly activated" out of the zero-voltage state, with a corresponding reduction in $\ensuremath{\tau}$. The results are well explained by numerical simulations.

The lifetime of the zero-voltage state of a current-biased Josephsonjunction shunted by a transmission line has been measured in the thermalregime. As the length of the line is increased /ital in/ /ital situ/, the lifetime ismodulated in an oscillatory pattern. The amplitude, period, phase, and tailingoff of the modulation is the first direct evidence for the oscillations of theparticle in the well before escape which are implied by Kramer'senergy-diffusion model for the escape from a metastable state.