We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born-Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then workout an analog of Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement at finite moments and its subsequent revivals (entanglement sudden death and entanglement sudden birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

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). Using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflection (MAR) regime, we find a significant difference of the subgap current structure compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose lengths significantly exceed the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the distance ?m between the static Andreev levels eVn=n?m. Moreover, the averaged IVC follows the powerlike behavior rather than the exponential one 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 having lengths 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 interlevel distance eVn=?m/n rather than the gap subharmonics 2?/n.

The specific property of a planar tunnel junction with thin-film diffusive plates and long enough leads is an essential enhancement of its transmission coefficient compared to the bare transparency of the tunnel barrier [1, 2]. In voltage-biased junctions, this creates favorable conditions for strong nonequilibrium of quasiparticles in the junction plates and leads, produced by multiparticle tunneling. We study theoretically the interplay between the nonequilibrium and relaxation processes in such junctions and found that nonequilibrium in the leads noticeably modifies the current-voltage characteristic at eV > 2 Delta, especially the excess current, whereas strong diffusive relaxation restores the result of the classical tunnel model. At eV <= 2 Delta, the diffusive relaxation decreases the peaks of the multiparticle currents. The inelastic relaxation in the junction plates essentially suppresses the n-particle currents (n > 2) by the factor n for odd and n/2 for even n. The results may be important for the problem of decoherence in Josephson-junction based superconducting qubits.

We present a theory for the current shot noise in long diffusive SNS structures with low-resistive interfaces at arbitrary temperatures. In such structures, the noise is mostly generated by normal electron scattering in the N-region. Whereas the I-V characteristics are approximately described by Ohm's law, the current noise reveals all characteristic features of the MAR regime: "giant" enhancement at low voltages, pronounced SGS, and excess noise at large voltages. The most spectacular feature of the noise in the incoherent MAR regime is a universal finite noise level at zero voltage and at zero temperature, S= 4Δ/3R. This effect can be understood as the result of the enhancement of the effective charge of the carriers, q^ eff=2Δ/V, or, alternatively, as the effect of strongly non-equilibrium quasiparticle population in the energy gap region with the effective temperature T_0=Δ/3. Under the condition of dominant electron-electron scattering, the junction undergoes crossover to the hot electron regime, with the effective temperature of the subgap electrons decreasing logarithmically with the voltage. Calculation of the noise power has been done on the basis of circuit theory of the incoherent MAR.

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. (C) 2014 Elsevier B. V. All rights reserved.

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.

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.

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 enhanced values of the subgap current in tunneling 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.

We calculate analytically the full counting statistics for a short normally conducting diffusive wire connecting a normal reservoir and a short superconductor-normal metal-superconductor junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference phi across the junction and approaches the normal-state value at phi = pi. At T = 0 and at applied voltage much smaller than the proximity gap Delta(phi), the current noise P-I doubles and the third current cumulant C-3 is 4 times larger compared to the normal state; at eV >> Delta(phi) they acquire large excess components. At the gap edge, eV = Delta(phi) the differential shot noise dP(I)/dV exhibits sharp peak, while the differential Fano factor dP(I)/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 = Delta(phi); the zero-bias slope of C-3(V) is much larger (up to 5 times) than at the zero temperature.

We present a detailed theory for the Andreev level qubit, a 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 a path integral method. We also derive a kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are nonlinear due to the fermionic nature of the Andreev states, leading to slow nonexponential relaxation and dephasing of the qubit at temperatures smaller than the qubit level spacing.

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and readout of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits and discuss the relevant SQUID parameters for qubit operation and readout.

We present theory for a current shot noise in mesoscopic diffusive superconductor-normal metal-superconductor (SNS) junctions. The current shot noise is tremendously enhanced at small applied voltage, V < Delta/c, due to the mechanism of multiple Andreev reflection (MAR), which creates long correlated trains of transmitted electrons. The central result for the MAR regime is a universal value for the noise power in the limit of small voltage and at zero physical temperature, which corresponds to the effective noise temperature of the order of superconducting energy gap Delta. At very small voltage, MAR is destroyed by inelastic relaxation, consequently, the level of noise reduces and approaches at V = 0 the thermal noise value. We investigate the suppression of MAR by inelastic scattering processes and analyze the crossover from the MAR regime to a hot electron regime.

A theory of coherent multiple Andreev reflections (MAR) is developed for superconductor-normal-metal-superconductor interferometers. We consider a Y-shaped normal-electron-beam splitter connecting two superconducting reservoirs, where the two connection points to the same superconductor can have different phases. The current is calculated in the quantum transport regime as a function of applied voltage and phase difference, I(V,phi). MAR in interferometers incorporate two features: interference in the arms of the splitter, and interplay with Andreev resonances. The latter feature yields enhancement of the subgap current and current peaks with phase-dependent positions and magnitudes. The interference effect leads to suppression of the subgap current and complete disappearance of the current peaks at phi=pi. The excess current at large voltage decreases and changes sign with increasing phase difference.

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.

The research of V. P. Galaiko, Fiz. Nizk. Temp. 19, 123 (1993) [Low Temp. Phys. 19, 87 (1993)] on electronic orbital effects in samples of a high-Tc superconductor (Y–Ba–Cu–O) in the normal state is continued for the case of dc galvanomagnetic effects. The conductivity tensor, resistivity, and Hall coefficient are calculated. The results agree qualitatively with experiment.

The dynamics of an rf SQUID with a one-mode point contact is analyzed. The state of Andreev levels in the contact can be measured by measuring flux oscillations through the SQUID.

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.

Spectral density of current fluctuations at zero frequency is calculated for a long diffusive SNS junction with low-resistive interfaces. At low temperature, T << Delta, the subgap shot noise approaches linear voltage dependence, S=(2/ 3R)(eV + 2Delta), which is the sum of the shot noise of the normal conductor and voltage independent excess noise. This result can also be interpreted as the 1/3-suppressed Poisson noise for the effective charge q = e(1+2Delta/eV) transferred by incoherent multiple Andreev reflections (MAR). At higher temperatures, anomalies of the current noise develop at the gap subharmonics, eV = 2Delta/n. The crossover to the hot electron regime from the MAR regime is analyzed in the limit of small applied voltages.