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We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. We modulate the magnetic flux through a superconducting quantum interference device, attached to a quarter-wavelength resonator, with frequencies $n\omega$ close to multiples, $n=2,\,3,\,4,\,5$, of the resonator fundamental mode and observe intense output radiation at $\omega$. The output field manifests $n$-fold degeneracy with respect to the phase, the $n$ states are phase shifted by $2\pi/n$ with respect to each other. Our demonstration verifies the theoretical prediction by Guo et al. in PRL 111, 205303 (2013), and paves the way for engineering complex macroscopic quantum cat states with microwave photons.

We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_B T \ll \hbar\omega$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\omega/2\pi \sim 5\,$GHz, when the resonator was driven by a current at $3\omega$ with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by $120^\circ$. The downconversion from $3\omega$ to $\omega$ is strongly enhanced by resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.

We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal metal region (N), which is controlled by the gate induced potential barrier (I). The calculations were performed using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflections (MAR) regime. We find significant difference of the subgap current structure in these junctions compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose length significantly exceeds the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the difference $\delta_m$ between the static Andreev levels, $eV_n = n\delta_m$. Moreover, the averaged IVC follows the power rather than exponential behavior, and has a universal scaling with the junction transparency. This result is qualitatively understood using an analytical approach based on the concept of resonant MAR trajectories. In shorter junctions whose length is comparable to the coherence length, the IVC has an exponential form common for point contacts, however the current structures appear at the subharmonics of the Andreev interlevel distance, $eV_n = \delta_m/n$ rather than the gap subharmonics $2\Delta/n$., Comment: 10 pages, 11 figures, submitted to Phys. Rev. B

We develop a theory for the current-voltage characteristics of diffusive superconductor-normal metal-superconductor Josephson junctions with resistive interfaces and the distance between the electrodes smaller than the superconducting coherence length. The theory allows for a quantitative analytical and numerical analysis in the whole range of the interface transparencies and asymmetry. We focus on the regime of large interface resistance compared to the resistance of the normal region, when the electron-hole dephasing in the normal region is significant and the finite length of the junction plays a role. In the limit of strong asymmetry we find pronounced current structures at the combination subharmonics of $\Delta+\Delta_g$, where $\Delta_g$ is the proximity minigap in the normal region, in addition to the subharmonics of the energy gap $2\Delta$ in the electrodes. In the limit of rather transparent interfaces, our theory recovers a known formula for the current in a short mesoscopic connector - a convolution of the current through a single-channel point contact with the transparency distribution for an asymmetric double-barrier potential., Comment: 10 pages, 3 figures

We propose and demonstrate a new read-out technique for a superconducting qubit by dispersively coupling it to a Josephson parametric oscillator. We employ a tunable quarter-wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with $185\pm15$ photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot readout performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing., Comment: 11 pages, 5 figures

The formation of quasiparticle zero-energy bound states at surfaces and interfaces of high-Tc superconductors is a direct consequence of the d-wave symmetry of the order parameter. In many cases it is possible to understand the novel physics appearing at surfaces/interfaces of d-wave superconductors by a simple consideration of the specific properties of the zero-energy states. Here we discuss how the large zero-energy density of states makes breaking of time-reversal symmetry energetically favorable, both at surfaces and at Josephson junctions. 2001 Elsevier Science B.V. All rights reserved.

Andreev bound states in superconducting quantum point contacts (QPC) can be accessed for manipulation and measurement by embedding the QPC in a superconducting loop. We discuss the characteristics of such a device suitable for qubit operation, methods of manipulations with the Andreev levels, and qubit coupling.

We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of 8 superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate mode of operation. Phase sensitive amplification-deamplification is also measured in the degenerate mode and yields a maximum gain of 37 dB. The compression point obtained is 18 dB above what would be obtained with a single SQUID of the same inductance, due to the smaller nonlinearity of the SQUID array., 7 pages, 4 figures, 23 references

We present detailed theory of parametric resonance in high quality tunable superconducting cavity. Nonlinear amplification of classical signals and quantum noise characteristics are calculated for broad range of device parameters below and above parametric threshold. © OSA 2014.

The influence of a noisy environment on coherent transport in Andreev states through a point contact between two superconductors is considered. The amount of dephasing is estimated for a microwave-activated quantum interferometer. Possibilities of experimentally investigating the coupling between a superconducting quantum point contact and its electromagnetic environment are discussed.

The formation of bound states at surfaces of materials with an energy gap in the bulk electron spectrum is a well known physical phenomenon. At superconductor surfaces, quasiparticles with energies inside the superconducting gap $\Delta$ may be trapped in bound states in quantum wells, formed by total reflection against the vacuum and total Andreev reflection against the superconductor. Since an electron reflects as a hole and sends a Cooper pair into the superconductor, the surface states give rise to resonant transport of quasiparticle and Cooper pair currents, and may be observed in tunneling spectra. In superconducting junctions, these surface states may hybridize and form bound Andreev states, trapped between the superconducting electrodes. In d-wave superconductors, the order parameter changes sign under $90^o$ rotation and, as a consequence, Andreev reflection may lead to the formation of zero energy quasiparticle bound states, midgap states (MGS). The formation of MGS is a robust feature of d-wave superconductivity and provides a unified framework for many important effects which will be reviewed: large Josephson current, low-temperature anomaly of the critical Josephson current, $\pi$-junction behavior, $0\to \pi$ junction crossover with temperature, zero-bias conductance peaks, paramagnetic currents, time reversal symmetry breaking, spontaneous interface currents, and resonance features in subgap currents. Taken together these effects, when observed in experiments, provide proof for d-wave superconductivity in the cuprates., Comment: 52 pages, 20 figures. Review article under consideration for publication in Superconductor Science and Technology

We report the results of an investigation of the effect of the superconducting bound states on coherent multiple Andreev reflections in quantum SNS junctions. A rich resonant structure of the current, associated with the bound states and consisting of peaks, onsets and oscillations, is found by numerical calculations. Positions of the current structures are not given by subharmonics of the energy gap but rather determined by the junction geometry. We present analytical classification of the resonant current structures and calculate their positions and amplitudes. We show that the resonant current structures in three-terminal SNS interferometers can be controlled by external magnetic flux.

We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30 nm, exhibits a record high magnitude of 800 nA at low temperature that comes close to the theoretically expected value. The critical current in all other devices is typically reduced compared to the theoretical values. The excess current is consistent with the normal resistance data and agrees well with the theory. The subgap current shows a large number of structures; some of them are identified as subharmonic gap structures generated by multiple Andreev reflection. The other structures, detected in both suspended and nonsuspended devices, have the form of voltage steps at voltages that are independent of either the superconducting gap or length of the wire. By varying the gate voltage in suspended devices, we are able to observe a crossover from typical tunneling transport at large negative gate voltage, with suppressed subgap current and negative excess current, to pronounced proximity junction behavior at large positive gate voltage, with enhanced Josephson current and subgap conductance as well as a large positive excess current., 12 pages, 15 figures

The incoherent regime of Multiple Andreev Reflections (MAR) is studied in long diffusive SNS junctions at applied voltages larger than the Thouless energy. Incoherent MAR is treated as a transport problem in energy space by means of a circuit theory for an equivalent electrical network. The current through NS interfaces is explained in terms of diffusion flows of electrons and holes through tunnel and Andreev resistors. These resistors in diffusive junctions play roles analogous to the normal and Andreev reflection coefficients in OTBK theory for ballistic junctions. The theory is applied to the subharmonic gap structure (SGS); simple analytical results are obtained for the distribution function and current spectral density for the limiting cases of resistive and transparent NS interfaces. In the general case, the exact solution is found in terms of chain-fractions, and the current is calculated numerically. SGS shows qualitatively different behavior for even and odd subharmonic numbers, and the maximum slopes of the differential resistance correspond to the gap subharmonics. The influence of inelastic scattering on the subgap anomalies of the differential resistance is analyzed., 14 pages, 9 figures, title and text revised, to appear in PRB

Single atom junctions between superconducting niobium leads are produced using the Mechanically Controllable Break Junction technique. The current-voltage characteristics of these junctions are analysed using an exact formulation for a superconducting quantum point contact. For tunnelling between two single atoms with a sufficiently large vacuum barrier, it is found that a single channel dominates the current, and that the current-voltage characteristic is described by the theory, without adjustable parameters. For a contact of a single Nb atom it is shown that five conductance channels contribute to the conductance, in agreement with the number expected based on the number of valence orbitals for this d-metal. For each of the channels the transmission probability is obtained from the fits and the limits of accuracy for these numbers are discussed., 11 pages; submitted to Phys. Rev. B

We study the dc conductance and current fluctuations in mesoscopic diffusive SNS junctions at subgap applied voltages $\mathrm{eV}l2\ensuremath{\Delta}$. We find that in spite of the multiple Andreev reflections, the current-voltage characteristic of a long SNINS structure obeys Ohm's law. At the same time, non-equilibrium heating of subgap electrons produces giant shot noise with pronounced subharmonic gap structure which corresponds to stepwise growth of the effective transferred charge. At $\mathrm{eV}\ensuremath{\rightarrow}0$, the shot noise approaches the magnitude of the Johnson-Nyquist noise with the effective temperature ${T}^{\ensuremath{\star}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/3$. We analyze the role of inelastic scattering and present a criterion of strong nonequilibrium.

We calculate the current-voltage characteristics (IVC) of a biased superconducting junction with a tunnel resonance. Within a simple one-dimensional model we discuss how the IVCs depend on the position and width of the resonance. We consider both subgap region and excess current. The results provide a possible explanation of the anomaly in the onset of c-axis current in recent experiments on intrinsic Josephson effect in BSCCO.

It is found that the dc Josephson current in a ballistic superconductor{endash}normal-metal{endash}superconductor junction connected to an electron reservoir does not decay with the length of the junction if voltage is applied between the reservoir and the junction. At finite temperature, this nonequilibrium Josephson current is proportional to the applied voltage and saturates at eV{gt}{Delta} at a level typical for the critical current of short junctions. In asymmetric junctions the current-phase dependence is {pi} periodic. {copyright} {ital 1997} {ital The American Physical Society}

We present the first measurements of the viscosity of superfluid {sup 3}He in magnetic fields up to 15 T , at temperatures down to 2 mK along the melting curve, using an assumption for the temperature dependence of the normal density. At fields higher than 4 T , the viscosity shows a minimum in the A{sub 1} phase, and reaches a local maximum at the A{sub 2} transition which becomes global at 14.6 T . The sharp decrease just below the A{sub 1} transition can be understood within the Ginzburg-Landau framework and is consistent with both theory and experiments in lower fields. At temperatures below the minimum, the viscosity in the A{sub 1} phase is dominated by a term with T{sup {minus}2} dependence. Additionally, we have calculated the temperature dependence of the viscosity tensor in the low temperature limit using the method of temperature asymptotes. {copyright} {ital 1997} {ital The American Physical Society}

Multiple Andreev scattering in single-mode superconducting junctions with arbitrary normal electron transparency 01 is studied in the limit of low applied voltage eV\ensuremath{\ll}\ensuremath{\Delta}. A quasiclassical approach is developed for investigation of the dense lattice of inelastic sidebands associated with multiple Andreev scattering, which gives a global description of inelastic-scattering amplitudes and spectral distribution of the current. The crossover from the contact to the tunnel regime is investigated for the dc current and ac Josephson current as function of junction transparency and applied voltage. A mesoscopic interference effect in junctions with intermediate transparency is discussed. This effect shows up in oscillating features of the current of thermal excitations.

We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the SQUID attached to the cavity, and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum statistical properties of the noise are addressed such as squeezing spectra, second order coherence, and two-mode entanglement., Comment: 25 pages, 17 figures

We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting quarter wavelength resonator, and is terminated by a flux-tunable superconducting quantum interference device. We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in situ by the applied dc flux. We also suggest how to cancel the effect of by adding a small dc flux and a pump tone at twice the pump frequency.

We report conductance and supercurrent of InAs nanowires coupled to Al-superconducting electrodes with short channel lengths and good Ohmic contacts. The nanowires are suspended 15 nm above a local gate electrode. The charge density in the nanowires can be controlled by a small change in the gate voltage. For large negative gate voltages, the number of conducting channels is reduced gradually, and we observe a stepwise decrease of both conductance and critical current before the conductance vanishes completely.

We consider the supercurrent flow through a gated two-dimensional normal constriction confined between superconducting electrodes. Photon-assisted Landau-Zener transitions between Andreev bound states in the constriction are shown to give rise to a series of reversals in the direction of supercurrent flow.

Non-equilibrium excess noise of a short quasi one-dimensional constriction between two superconductors is considered. A general expression for the current-current correlation function valid for arbitrary temperatures and bias voltages is derived. This formalism is applied to a current-carrying quantum channel with perfect transparency. Contrary to a transparent channel separating two normal conductors, a weak link between two superconductors exhibits a finite level of noise. The source of noise is fractional Andreev scattering of quasiparticles with energies $|E|$ greater than the half-width $\Delta$ of the superconducting gap. For high bias voltages, $V \gg \Delta /e$, the relation between the zero-frequency limit of the noise spectrum, $S(0)$, and the excess current $I_{\text{exc}}$ reads $S(0)=(1/5)|e|I_{\text{exc}}$. As $\Delta \rightarrow 0$ both the excess noise and the excess current vanish linearly in $\Delta$, %$\propto \Delta$, their ratio being constant.

We study the microscopic structure of the Josephson current in a single-mode tunnel junction with a wide quasiclassical tunnel barrier. In such a junction each Andreev bound state carries a current of magnitude proportional to the {\em amplitude} of the normal electron transmission through the junction. Tremendous enhancement of the bound state current is caused by the resonance coupling of superconducting bound states at both superconductor-insulator interfaces of the junction. The possibility of experimental observation of the single bound state current is discussed., 11 pages, [aps,preprint]{revtex}

We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field. © 2012 American Physical Society., We acknowledge funding from Spanish MICINN Juan de la Cierva, FIS2009-12773-C02-01, and FIS2011-28851-C02-02; Basque Government IT472-10 and IT- 366-07; UPV/EHUUFI 11/55; SOLID, CCQED, and PROMISCE European projects.

A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er$^{3+}$ doped Y$_2$SiO$_5$ crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewdith of down to 75 MHz., Comment: 5 pages, 4 figures

We solve the coherent multiple Andreev reflection (MAR) problem and calculate current-voltage characteristics (IVCs) for Josephson SINIS junctions, where S are local-equilibrium superconducting reservoirs, I denotes tunnel barriers, and N is a short diffusive normal wire, the length of which is much smaller than the coherence length, and the resistance is much smaller than the resistance of the tunnel barriers. The charge transport regime in such junctions qualitatively depends on a characteristic value \gamma = \Delta \tau_d of relative phase shifts between the electrons and retro-reflected holes accumulated during the dwell time \tau_d. In the limit of small electron-hole dephasing \gamma << 1, our solution recovers a known formula for a short mesoscopic connector extended to the MAR regime. At large dephasing, the subharmonic gap structure in the IVC scales with 1/ \gamma, which thus plays the role of an effective tunneling parameter. In this limit, the even gap subharmonics are resonantly enhanced, and the IVC exhibits portions with negative differential resistance., Comment: 8 pages, 3 figures, typos corrected, to be published in Phys. Rev. B

In highly resistive superconducting tunnel junctions, excess subgap current is usually observed and is often attributed to microscopic "pinholes" in the tunnel barrier. We have studied the subgap current in superconductor-insulator-superconductor (SIS) and superconductor-insulator-normal-metal (SIN) junctions. In Al/AlOx/Al junctions, we observed a decrease of 2 orders of magnitude in the current upon the transition from the SIS to the SIN regime, where it then matched theory. In Al/AlOx/Cu junctions, we also observed generic features of coherent diffusive Andreev transport in a junction with a homogenous barrier. We use the quasiclassical Keldysh-Green function theory to quantify single- and two-particle tunneling and find good agreement over 2 orders of magnitude in transparency. We argue that our observations rule out pinholes as the origin of the excess current., 4 pages, 4 figures

We report the observation of photon generation in a microwave cavity with a time-dependent boundary condition. Our system is a microfabricated quarter-wave coplanar waveguide cavity. The electrical length of the cavity is varied using the tunable inductance of a superconducting quantum interference device. It is measured in the quantum regime, where the temperature is significantly less than the resonance frequency (~ 5 GHz). When the length is modulated at approximately twice the static resonance frequency, spontaneous oscillations of the cavity field are observed. Time-resolved measurements of the dynamical state of the cavity show multiple stable states. The behavior is well described by theory. Connections to the dynamical Casimir effect are discussed., 5 pages, 3 Figures

We present a theoretical analysis of the transition from thermal activation (TA) regime to the macroscopic quantum tunneling (MQT) regime of the decay from a metastable persistent current state in grain boundary junctions of cuprate superconductors. This transition is conventionally characterized by a single crossover temperature determined by the potential profile and dissipative mechanisms. It is shown that due to the existence of low energy bound states (mid-gap states) for various relative orientations of the crystal axes, there exists a window of parameters where one finds, with lowering temperature, an inverse crossover from MQT to TA, followed by a subsequent reentrance of MQT. It is shown that these predictions are in reasonable agreement with recent experiments.

We develop a theoretical description of non-adiabatic Josephson dynamics in superconducting junctions containing low energy quasiparticles. Within this approach we investigate the effects of midgap states in junctions of unconventional d-wave superconductors. We identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling, and connect this phenomenon to the experimental observations in Phys. Rev. Lett. 94, 087003 (2005). It is also shown that nonlinear Josephson dynamics can be defined by resonant interaction with midgap states reminiscent to nonlinear optical phenomena in media of two-level atoms., 16 pages, 2 figures

This paper presents a theoretical analysis of the recently realized tuneable coupler for superconducting phase qubits (R. C. Bialczak et al., Ref.\ \protect\onlinecite{Bialczak}). The coupling can be turned off by compensating a negative mutual inductance with a tuneable Josephson inductance. The main coupling in this system is of the $XX$ type and can be zeroed exactly, while there is also a small undesired contribution of the $ZZ$ type. We calculate both couplings as functions of the tuning parameter (bias current) and focus on the residual coupling in the OFF regime. In particular, we show that for typical experimental parameters the coupling OFF/ON ratio is few times $10^{-3}$, and it may be zeroed by proper choice of parameters. The remaining errors due to physical presence of the coupler are on the order of $10^{-6}$., 11 pages

Conventional models of Josephson junction dynamics rely on the absence of low energy quasiparticle states due to a large superconducting gap. With this assumption the quasiparticle degrees of freedom become "frozen out" and the phase difference becomes the only free variable, acting as a fictitious particle in a local in time Josephson potential related to the adiabatic and non-dissipative supercurrent across the junction. In this article we develop a general framework to incorporate the effects of low energy quasiparticles interacting non-adiabatically with the phase degree of freedom. Such quasiparticle states exist generically in constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. Furthermore, recent experiments have revealed the existence of spurious low energy in-gap states in tunnel junctions of conventional superconductors - a system for which the adiabatic assumption typically is assumed to hold. We show that the resonant interaction with such low energy states rather than the Josephson potential defines nonlinear Josephson dynamics at small amplitudes., Comment: 9 pages, 1 figure

Two-band models (one wide band and one narrow band close to the Fermi energy) and local-pair models (periodic Anderson model) of high-Tc superconductors give rise to the same equilibrium thermodynamics despite the different physical pictures underlying the models. The low-energy excitations in these models are, however, not of the same character, which leads to a qualitative difference in their non-equilibrium properties. In particular, this is true for the interband optical absorption at threshold. Using the Golden rule for absorption and a mean-field treatment of the superconducting state, we calculate the threshold absorption at zero temperature for three different cases: a two-band model without additional correlation besides the interband interaction between Cooper pairs; a two-band model with attractive correlation (negative-U) between electrons on the same site in the narrow band; and a local-pair model with the same correlation as in the previous model, but with a pair interaction due to the hybridization (in second order) of the wide band and the local states. In the two latter models (which are closely related), we assume that the local-pair correlation energy is much higher than Tc. In the uncorrelated case the absorption has a square-root singularity at threshold, which is due to the diverging density of states of the one-particle excitations. In the negative-U correlated cases no single-particle transitions are possible at threshold, and only direct two-photon two-particle processes are possible. Further, in the local-pair model the hybridization can act together with a photon, giving an additional one-photon two-electron threshold in the absorption.

We study the out-of-equilibrium current through a quantum dot which is placed between two superconducting leads held at fixed voltage bias, considering both cases of the absence and the presence of an additional normal lead connected to the dot. Using the nonequilibrium Keldysh technique, we focus on the subgap bias region, where multiple Andreev reflections are responsible for charge transfer through the dot. Attention is put on the dc current and on the first harmonics of the supercurrent. Varying the position and/or the width of the dot level, we first investigate the crossover between a quantum-dot and quantum point-contact regimes in the absence of a normal lead. We then study the effect of the normal electrode connected to the dot, which is understood to lead to dephasing, or alternatively to induce reverse proximity effect. By increasing the dot coupling to the normal probe, we show the full crossover from zero dephasing to the incoherent case. We also compute the Josephson current in the presence of the normal lead and find it in excellent agreement with the values of the nonequlibrium current extrapolated at zero voltage.

Non-dissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, so-called Andreev bound states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy., Published version; 4+ pages, 3 figures

We investigate the performance of a three qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where the dephasing rate is low. Numerical studies in previous work have however shown that the code does increase the fidelity of the encoded state even in the presence of high error probability, during both storage and processing. In this work we give analytical expressions for the fidelity of such a code. We consider two specific schemes for qubit-qubit interaction realizable in superconducting systems; one $\sigma_z\sigma_z$-coupling and one cavity mediated coupling. With these realizations in mind, and considering errors during storing as well as processing, we calculate the maximum operation time allowed in order to still benefit from the code. We show that this limit can be reached with current technology., Comment: 10 pages, 8 figures

We investigate manipulation with Andreev bound states in Josephson quantum point contacts with magnetic scattering. The Rabi oscillations in the two-level Andreev subsystems are excited by resonant driving the direction of magnetic moment of the scatterer and by modulating the superconducting phase difference across the contact. The Andreev level dynamics is manifested by the temporal oscillation of the Josephson current, which is accompanied, in the case of magnetic manipulation, also by the oscillation of the Andreev states spin polarization. The interlevel transitions obey a selection rule that forbids manipulations in a certain region of external parameters and results from specific properties of Andreev bound states in magnetic contacts: 4pi periodicity with respect to the superconducting phase and strong spontaneous spin polarization.

We formulate a theoretical framework to describe multiparticle current transport in planar superconducting tunnel junctions with diffusive electrodes. The approach is based on direct solving of quasiclassical Keldysh-Green function equations for nonequilibrium superconductors, and consists of a combination of a circuit theory analysis and improved perturbation expansion. The theory predicts much greater scaling parameter for the subharmonic gap structure of the tunnel current in diffusive junctions compared to the one in ballistic junctions and mesoscopic constrictions with the same barrier transparency., Comment: 18 pages, 6 figures, to be published in Supercond. Sci. Techn

We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux-biased dc superconducting quantum interference device attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is able to accommodate several qubits and allows one to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.

We calculate analytically the full counting statistics for a short normally conducting diffusive wire connecting a normal reservoir and a short superconductornormal metal-superconductor junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference φ across the junction and approaches the normal-state value at φ = π. At T = 0 and at applied voltage much smaller than the proximity gap ∆φ, the current noise PI doubles and the third current cumulant C3 is 4 times larger compared to the normal state; at eV ≫∆φ they acquire large excess components. At the gap edge, eV = ∆φ, the differential shot noise dPI/dV exhibits sharp peak, while the differential Fano factor dPI/dI turns to zero along with the differential resistance, which reflects the transmission resonance associated with the singularity of the density of states. At nonzero temperature, C3 shows a non-monotonous voltage dependence with a dip near eV = ∆φ; the zero-bias slope of C3(V ) is much larger (up to 5 times) than at the zero temperature. During last few years the statistics of quantum and thermal fluctuations of the electric current in mesoscopic systems has been attracted a rapidly growing attention. It was recognized that measuring the fluctuation properties of mesoscopic conductors provide unique and important information about correlations and statistics of charge carriers, the information that is not accessible through conventional conductance measurements. An adequate and powerful

We calculate the subgap current in planar superconducting tunnel junctions with thin-film diffusive leads. It is found that the subharmonic gap structure of the tunnel current scales with an effective tunneling transparency which may exceed the junction transparency by up to two orders of magnitude depending on the junction geometry and the ratio between the coherence length and the elastic scattering length. These results provide an alternative explanation of anomalously high values of the subgap current in tunnelling experiments often ascribed to imperfection of the insulating layer. We also discuss the effect of finite lifetime of quasiparticles as the possible origin of additional enhancement of multiparticle tunnel currents., 4 pages, 4 figures, to be published in Phys. Rev. B

Theoretical investigation of a chain of loop-shaped charge qubits, interacting via joint Josephson junctions is performed. Neighbouring qubits are coupled to each other only when the bias current through the joint Josephson junction is switched on. The maximum coupling strength is estimated and how to perform a universal set of quantum gates is shown.

We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular we focus attention of dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time., 20 pages, 7 figures. To be published in J. Phys.: Condensed Matter, 18 (2006) Special issue: Quantum computing

We study nonequilibrium effects in current transport through voltage biased tunnel junction with long diffusive superconducting leads at low applied voltage, $eV \ll 2\Delta$, and finite temperatures. Due to a small value of the Josephson frequency, the quasiparticle spectrum adiabatically follows the time evolution of the superconducting phase difference, which results in the formation of oscillating bound states in the vicinity of the tunnel junction (Andreev band). The quasiparticles trapped by the Andreev band generate higher even harmonics of the Josephson ac current, and also, in the presence of inelastic scattering, a non-equilibrium dc current, which may considerably exceed the dc quasiparticle current given by the tunnel model. The distribution of travelling quasiparticles also deviates from the equilibrium due to the spectrum oscillations, which results in an additional contribution to the dc current, proportional to $\sqrt{V}$., Comment: 11 pages, 7 figures, to be published in Phys. Rev. B

We investigate the design and functionality of a network of loop-shaped charge qubits with switchable nearest-neighbor coupling. The qubit coupling is achieved by placing large Josephson junctions at the intersections of the qubit loops and selectively applying bias currents. The network is scalable and makes it possible to perform a universal set of quantum gates. The coupling scheme allows gate operation at the charge degeneracy point of each qubit, and also applies to charge-phase qubits. Additional Josephson junctions included in the qubit loops for qubit readout can also be employed for qubit coupling., 23 pages, 4 figures

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances., 4 pages, 4 figures

We present detailed theory for Andreev level qubit, the system consisting of a highly transmissive quantum point contact embedded in a superconducting loop. The two-level Hamiltonian for Andreev levels interacting with quantum phase fluctuations is derived by using the path integral method. We also derive kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are non-linear due to fermionic nature of the Andreev states, leading to slow non-exponential relaxation and dephasing of the qubit at temperature smaller than the qubit level spacing., 22 pages, 7 figures