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Exact traveling soliton solutions for the Josephson nonlinear Left-handed transmission line (NL-JLHTL) based on the periodic structure of an array of Josephson junctions (JJs) are investigated. The nonlinearity of the Josephson left-handed transmission line (JLHTL) is due to the highly nonlinear nature of the JJs that provide the shunt inductances required to realize an LHTL. Applying the generalized Ricati methods, we analytically and successfully derive exact traveling kink solitons, bright and dark solitary wave solutions on this network. The left-handedness of the line is explicitly confirmed in numerical simulations with the existence of bright and dark soliton solutions in good agreement with analytical predictions.

Purpose: The purpose of this report is to present the similarities and differences between modified sine-Gordon models used in description of the curved Josephson junctions. The leading dynamical variable in this system is a gauge invariant phase difference of the macroscopic wave functions of the superconducting electrodes that form the junction. Findings: The main finding of this article is the observation that in the model used in description of junctions with quickly varying curvatures the significant part of the kink energy is confined in the curved regions of the junction. Research limitations/implications: The paper is limited to the description of the dynamics of fluxions in the long Josephson junctions. These junctions due to small transverse sizes (smaller than the Josephson penetration depth) can be considered as a one dimensional systems. Practical implications: It seems that junctions with appropriate geometry will find applications in future electronic devices. It is expected that curved Josephson junctions can be used in order to store a binary data. Originality/value: The main idea of the paper is to use a Riemann geometry in order to describe the influence of the curvature on the kink motion in the junction.

The dynamics of Josephson tunneling for weakly interacting coupled Bose–Einstein condensates in a double well is investigated using the two mode approximation. We introduce a polar-coordinate transformation of the variables describing the imbalance of the particle populations in symmetric and asymmetric traps. It is found that by a suitable adjustment of the initial imbalance in the double well and the interaction strength of the particles it is possible to delay the oscillations of the particles from one well to another.

We suggest a solution in principle for implementation of bi-superconducting quantum interference devices (bi-SQUIDs) on the basis of bicrystalline technology for high-temperature Josephson junctions. Optimization of the device design and parameters is discussed. Examples of the possible bi-SQUID layouts are considered.

By considering quantum impurities in the superconductors, we mimic their influences on the phase transition in a Josephson junction. It is found that the impurities in the superconductors can take nontrivial effects to the Josephson phase transition, and they are able to promote or hinder the 0 → π phase-transition phenomenon. Namely, for the 0 ( π ) junction with one impurity, it has an opportunity to become a π (0) junction, following the adjustment of the impurity-superconductor coupling. However, when each superconductor has an embedded impurity, their effect on the phase transition tends to become weak. We believe that this work can be helpful in understanding the contribution of impurities to the Josephson phase transition.

We present a detailed theoretical description of quantum coherent electron transport in voltage-biased cross-like Andreev interferometers. Making use of the charge conjugation symmetry encoded in the quasiclassical formalism, we elucidate a crucial role played by geometric and electron-hole asymmetries in these structures. We argue that a non-vanishing Aharonov-Bohm-like contribution to the current $I_S$ flowing in the superconducting contour may develop only in geometrically asymmetric interferometers making their behavior qualitatively different from that of symmetric devices. The current $I_N$ in the normal contour -- along with $I_S$ -- is found to be sensitive to phase-coherent effects thereby also acquiring a $2\pi$-periodic dependence on the Josephson phase. In asymmetric structures this current develops an odd-in-phase contribution originating from electron-hole asymmetry. We demonstrate that both phase dependent currents $I_S$ and $I_N$ can be controlled and manipulated by tuning the applied voltage, temperature and system topology, thus rendering Andreev interferometers particularly important for future applications in modern electronics.

The gauge invariant phase difference between superconducting electrodes is a dominating dynamical degree of freedom in the Josephson junction. This rapport concerns the influence of the curvature of the junction on the dynamic of this field variable. The effects of curvature are discussed in the long and large area junctions. In particular the dynamics of the fluxion and the kink front are studied.

We theoretically investigate the magnetization inside a normal metal containing the Rashba spin-orbit interaction (RSOI) induced by the proximity effect in an s-wave superconductor/normal metal/ferromagnetic metal/s-wave superconductor (S/N/F/S) Josephson junction. By solving the linearized Usadel equation taking account of the RSOI,we find that the direction of the magnetization induced by the proximity effect in N can be reversed by tuning the RSOI.Moreover, we also find that the direction of the magnetization inside N can be reversed by changing the superconducting phase difference, i.e., Josephson phase. From these results, it is expected that the dependence of the magnetization on the RSOI and Josephson phase can be applied to superconducting spintronics., 20 pages, 5 figures

Within the Bogoliubov–de Gennes theory we have studied the transport properties of disordered Josephson systems with several superconducting electrodes weakly coupled through a normal region. The scattering-matrix approach has been applied for arbitrary geometries of the normal region to analyze the quasi-particle spectra and current-phase relations (CPRs). The dependence of CPRs on the system geometry and its lengths reveals itself in the coefficients of the scattering matrix in the connecting normal area. This approach is applicable to mesoscopic superconducting structures with a normal weak link which appears to be small compared to the superconducting coherence length. The possible applications of our results and typical experimental examples have been discussed.

The kink solution in the long Josephson junction is studied. The perturbation scheme of constructing the fluxon solution in curved junction is formulated. The prediction from the perturbation scheme is compared with the prediction that follows from the numerical studies of the complete field model.

We investigate dynamical phase transitions that are induced by interspecies interaction in a two-species bosonic Josephson junctions (BJJ), based on semi-classical theory. In zero-phase mode, similar to the case of a single-species BJJ, we observe the well-known dynamical phase transition from Josephson oscillation to self-trapping, which can be induced by both enhanced repulsive and attractive interspecies interactions. In π phase mode, dynamical phase transitions are even more interesting and counter-intuitive. We characterize a dynamical phase transition with the merging of two separate phase space domains into one, which is induced by increasing repulsive interspecies interaction. On the other hand, we find that by increasing attractive interspecies interaction, a phase separation of two formally overlapped phase space domains will occur. At last, we reveal that these intriguing dynamical phase transitions are caused by different kinds of bifurcations.

By use of a recently developed multi-scale simulation method, we re-investigate terahertz wave emission with motions of Josephson vortices, as a possible mechanism for enhancing the emitted power. Results show that there appears a strong wave emission around the n = 2 cavity mode (one-wavelength mode), when motions of vortices and cavity modes are resonate.

The transition dynamics of photons between an optical soliton in a nonlinear dielectric waveguide and a spatially coupled surface-plasmon excitation on a parallel flat metal surface can be formulated in analogy to that of a Josephson junction of two-level (double-well) Bose-Einstein condensates, albeit with a nonlinear coupling that inherently depends on the population imbalance of the levels. The present work demonstrates that asymmetric Rosen-Zener-like transitions can be obtained through this optical Josephson junction, by turning on and off the coupling across a hyperbolically varying separation between the soliton and the surface-plasmon. The transitions can generate full population transfer, population splitting, or merging between the quasistationary initial and final states, which are defined by a fixed population imbalance in the decoupled limit. Transitions from a pure soliton or pure surface-plasmon initial state are found to be robust against the relative phase, whereas the transitions from an initial state with mixed population depend strongly on the relative phase. The soliton-surface-plasmon system also bears similarities to the spatially coupled optical waveguides which are introduced further as the classical analogs of the spatial adiabatic passage and stimulated Raman adiabatic passage mechanisms in quantum and atom optics., Scientific and Technological Research Council of Turkey (TÜBİTAK); Turkish Academy of Sciences Associate Member Research Grant

The source-sink algorithm presented in Sect. 3.3 allows us to perform time-resolved simulations of quantum transport that scale linearly with the required maximum simulation time.

After the introduction to the JOSEPHSON junction (Chap. 10) and the presentation of its role in SQUIDs (Chap. 11), this chapter introduces effects resulting from application of a magnetic field B ext to the junction itself.

The JOSEPHSON effect results from the passage of “particles” COOPER pairs, and not of individual electrons, between two superconductors separated by an insulating barrier (SIS), by a normal metal (SNS), by a simple constriction in the superconductor (SCS or “weak link”) or by a ferromagnetic layer (SFS).

We theoretically investigate the effects of exchange splitting, electric field and strain on the supercurrent in silicene-based Josephson junctions. It is observed that a $0\ensuremath{-}\ensuremath{\pi}$ transition is induced by the exchange splitting, and the critical supercurrent at the transition point is nonvanishing. Owing to the unique buckling structure of silicene, the supercurrent can be effectively controlled by the electric field. For the strain dressed supercurrent, it is revealed that the current-phase relation is profoundly influenced by the strain, and the supercurrent exhibits a switch effect with increasing the strength of strain. These findings will potentially provide some intriguing insights into the correlated transport in silicene-based Josephson junctions.

AC Josephson voltage standards are typically based on series arrays of overdamped Josephson junctions, which are presently realized using an Nb x Si 1-x barrier at PTB. The characteristic parameters of these SNS-like junctions can be tuned by the Nb content and the thickness of the barrier over a wide range for operation from 10 GHz to 70 GHz. Based on these junctions, we developed binary-divided 10 V arrays as well as pulse-driven arrays for 1 V output voltages.

We investigate experimentally the retrapping of the phase in a $\ensuremath{\varphi}$ Josephson junction upon return of the junction to the zero-voltage state. Since the Josephson energy profile ${U}_{0}(\ensuremath{\psi})$ in $\ensuremath{\varphi}$ JJ is a $2\ensuremath{\pi}$ periodic double-well potential with minima at $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}\phantom{\rule{0.28em}{0ex}}mod\phantom{\rule{0.28em}{0ex}}2\ensuremath{\pi}$, the question is at which of the two minima $\ensuremath{-}\ensuremath{\varphi}$ or $+\ensuremath{\varphi}$ the phase will be trapped upon return from a finite voltage state during quasistatic decrease of the bias current (tilt of the potential). By measuring the relative population of two peaks in escape histograms, we determine the probability of phase trapping in the $\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$ wells for different temperatures. Our experimental results agree qualitatively with theoretical predictions. In particular, we observe an onset of the butterfly effect with an oscillating probability of trapping. Unexpectedly, this probability saturates at a value different from 50% at low temperatures.

Experimental and theoretical studies of ferromagnet-superconductor hybrid systems consisting of a Josephson junction placed in the nonuniform field of submicron ferromagnetic particles are reviewed.

We consider a rotating Bose–Einstein condensate in an optical lattice in the regime in which the system Hamiltonian can be mapped onto a Josephson junction array. In an approximate scheme where the couplings are assumed uniform, the ground state energy is formulated in terms of the vortex configuration. Application of the method for the ladder case presented and the results are compared with Monte-Carlo method.

In this work, we consider controlling of logical states of Josephson memory cells (cryotrons) based on superconductor-insulator-superconductor (SIS) Josephson tunnel junctions by external current impulses. A mathematical model for the transitional processes that take place during direct logical transitions “0” → “1” and inverse logical transitions “1” → “0” is proposed. By means of mathematical modeling, we investigate transitional processes in cryotrons during the change of their logical state and obtain their transitional characteristics for operational temperatures T1=11.6 K and T2=81.2 K, close to the boiling temperatures of helium and nitrogen, respectively. It is shown that such memory cells can efficiently operate under the temperature T2=81.2 K. The behavior of the Josephson cryotrons as well as their operational stability is explored.

With the help of the exact diagonalization approach, the Josephson phase transition in a T-shaped double quantum-dot (QD) junction is theoretically investigated. It is found that when the intradot Coulomb interaction in one dot is super-strong, new Josephson phase-transition manner comes into being, in comparison with the case of two identical dots. Besides, owing to the different positions of the two dots, the super-strong Coulomb repulsions in them induce two phase-transition results, respectively. We believe that this work can be helpful in understanding how the super-strong Coulomb interaction influences the phase transition in the Josephson junction with embedded dots.

We study a transition from Rabi to Josephson oscillations in spinor Bose-Einstein condensates by calculating spin-1 two-dimensional Gross-Pitaevskii equations numerically. The transition appears in off-resonance caused by quadratic Zeeman effect in a magnetic field. It is a novel phenomenon combining magnetic resonance with Josephson effects due to quantum tunneling.

The resistive–capacitive–inductive-shunted (RCL-shunted) Josephson junction (RCLSJJ) shows chaotic behavior under some parameter conditions. This paper studies chaos control in the RCLSJJ based on the delayed feedback theory. Numerical results demonstrate that chaotic states in this junction can be controlled into stable periodic states by appropriately adjusting the feedback intensity and delay time.

We report on the fabrication and properties of sub-micron YBa2Cu3O7-x off-axis biepitaxial junctions. The vision behind this work is to set up a reliable nanotechnology processing to improve junctions' performances and reproducibility through the reduction of their size. We will illustrate the fabrication procedure employed and show the results obtained on samples where the transport parameters were tuned in a predictable way. Also, proofs of a clean barrier structure with few facets and low disorder were obtained.

The phase transition of Nb/Cu0.41Ni0.59/Nb triple layers from the normal to the superconducting state has been studied experimentally by measuring the temperature dependence of the electrical resistance, R(T). It is shown that the shape of the R(T) curves is different depending on the Cu0.41Ni0.59 thickness. To explain the experimental data we developed a qualitative model which makes more evident the interconnection between the superconducting phase transition and the 0 to  crossover in SFS structures.

The transient dynamics of long overlap Josephson junctions in the frame of the sine-Gordon model with a white noise source is investigated. The effect of noise delayed decay is observed for the case of overdamped sine-Gordon equation. It is shown that this noise induced effect, in the range of small noise intensities, vanishes for junctions lengths greater than several Josephson penetration length., Comment: 7 pages, 9 figures, to appear in Journ. of Bifurcation and Chaos, 2008

We investigate the dynamics of two sinusoidally coupled Josephson junction rotators to provide a clear knowledge of the behaviors in different regions of the parameter space. The dynamical states are identified, and the transitions among these states are studied. The properties of the current–voltage curves are investigated. Further more, we observed the chaotic states in some regions of parameter space. We conjecture it may caused by the competition of two periodic potentials: one is the external field, another is the interacting of two particles.

The relative phase of Bosonic Josephson junction in the Josephson regime of Bose-Hubbard model is tracked via the target attractor (‘synergetic’) feedback algorithm with the inter-well coupling parameter presented as a control function. The efficiency of our approach is demonstrated numerically for Gaussian and harmonic types of target phases.

A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semiclassic limit. The spectrum of Andreev bound states is obtained from the single valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position–particle-hole–spin space is constructed and shown to depend on only two parameters, namely, a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials., The work of F. S. B. and F. K. was supported by Spanish Ministerio de Economía y Competitividad (MINECO) through Project No. FIS2014-55987-P and the Basque Government under UPV/EHU Project No. IT-756-13. I. V. T. acknowledges support from the Spanish Grant No. FIS2013-46159-C3-1-P and from the “Grupos Consolidados UPV/EHU del Gobierno Vasco” (Grant No. IT578-13).

The number-phase quantization scheme of the capacitance coupling double Josephson junction mesoscopic circuit is given. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can be prepared.

We review the experimental realization of a single bosonic Josephson junction for ultracold gases, which was made possible by the generation of a precisely controllable double-well potential for Bose–Einstein condensates. We will focus on the comparison of the experimentally obtained data with the predictions of a many-body two-mode model and a mean-field description and show that the observed static, thermal and dynamical properties can be described in terms of classical equations.