Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.     

Fluxon interaction in a long Josephson junction

Fluxon interaction in a long Josephson junction with bias current and losses is investigated by means of a perturbational approach. A simple analytical theory of the congelation (bunching) of unipolar fluxons is presented. Asymptotic results are confirmed by numerical solutions. It is shown that a system of congealed fluxons reflects from an open end of the junction without being destroyed.     

Exact and numerical solutions to the perturbed sine-Gordon equation

We present numerical and analytic solutions to the perturbed sine-Gordon equation, which models long Josephson tunnel junctions. We make comparisons between numerical results and results obtained from perturbational methods. We present unstable, analytic kink solutions to the equation and further a solution, which is an array of kinks, corresponding to a solution, where the current through the junction is larger than the critical current.     

Magnetic field rectifiers using semicircular Josephson junctions

A novel method for rectifying alternating magnetic fields is demonstrated using fluxons in semicircular Josephson junctions. An external magnetic field applied parallel to the dielectric barrier of the semicircular junction has opposite polarities at the ends of the junction and supports penetration of opposite polarity fluxons into the junction in the presence of a constant dc bias. When the direction of the field is reversed, flux penetration is not possible and a flux-free state exists in the junction. Thus, effective rectification of an alternating magnetic field can be achieved in semicircular Josephson junctions. This unique phenomenon is specific to this geometry and can be employed in rf SQUID magnetometers.     

Steady oscillatory states of a finite Josephson junction

Under the assumption that solutions have traveling-wave form, time-periodic solutions are found for the Josephson phase equation for a finite-length tunnel junction with uniform current feed and linear loss term. Exact current-voltage characteristics are found and compared with simple approximations. The complete current-velocity and mean-width-velocity curves for isolated fluxons are found. Comparison with characteristics for a finite junction shows that end effects obtained from analysis of a circuit model of the junction shows that end effects introduce lower- and upper-current thresholds.     

DC current singularities in long Josephson tunnel junctions: Approximate solutions of the sine-Gordon equation with loss and bias

We construct approximate analytic solutions of the sine-Gordon equation with loss and bias, which describe the fluxon propagation in long overlap Josephson junctions. By these solutions a qualitative explanation of the main observed features of the DC current singularities can be easily obtained.     

Bound fluxon pair in one-dimensional SQUID array

We propose a one-dimensional array of superconducting quantum interference devices (SQUIDs) composed of three asymmetrically positioned Josephson junctions to realize a discrete double sine-Gordon (DSG) model. Two fluxons in this SQUID array attract each other and form bound states with internal oscillation modes. We conduct numerical simulations of a discrete DSG equation, and show that the period of the internal oscillation of a moving fluxon pair exhibits relativistic time dilation except near the speed of light. We also show that driving with a pure alternating current causes progressive motion of the bound fluxon pair even in the presence of dissipation.     

Dynamics of fluxons in Josephson junctions under the noise current action

The motion of magnetic flux quanta (fluxons) in long Josephson junctions (LJJ) under action of direct and random currents is under investigation. The velocity distribution function of fuxons is calculated which, even in the absence of the direct current component, is non-Gaussian. As a consequence, the current-voltage characteristic of a noise junction differs from that for a regular one. The dependence of the voltage difference on the current for junctions, both with and without the noisy current component, is shown to be non-monotonic. There is a good agreement between the calculation data and the numerical simulation results.     

RF impedance of intrinsic Josephson junction in flux-flow state with a periodic pinning potential and its optimum condition for RF radiation

We reported dynamics of Josephson vortices interacting with electromagnetic waves in strongly coupled long Josephson junctions stack, such as an intrinsic Josephson junction (IJJ), by numerical simulations based on coupled sine-Gordon equations considering a periodic pinning potential of sinusoidal form. The numerical simulation results for the influence of the electromagnetic waves on flux-flow properties show that the periodic pinning potential induces an in-phase motion of Josephson vortices over the junction stacks, which achieve high performances of IJJ flux-flow oscillator. In order to prove it from another viewpoint, we calculate RF impedance of long Josephson junction stacks in flux-flow state. A remarkable negative real part region of RF impedance appears at 1st harmonic step, it means that the long Josephson junction stacks in flux-flow state acts as an oscillator at the negative real part region. In this study, we evaluate the optimum condition for RF radiation with the periodic pinning potential.     

Effect of inductive and capacitive coupling on the current–voltage characteristic and electromagnetic radiation from a system of Josephson junctions

We have studied the current–voltage characteristic of a system of long Josephson junctions taking into account the inductive and capacitive coupling. The dependence of the average time derivative of the phase difference on the bias current and spatiotemporal dependences of the phase difference and magnetic field in each junction are considered. The possibility of branching of the current–voltage characteristic in the region of zero field step, which is associated with different numbers of fluxons in individual Josephson junctions, is demonstrated. The current–voltage characteristic of the system of Josephson junctions is compared with the case of a single junction, and it is shown that the observed branching is due to coupling between the junctions. The intensity of electromagnetic radiation associated with motion of fluxons is calculated, and the effect of coupling between junctions on the radiation power is analyzed.     

Analytical solution of fluxons in a non-homogeneous Josephson junction

In order to study the fluxon behavior in a Josephson junction, a dielectric with variable thickness was inserted between two superconductors, which can be position-dependent. An analytical solution of the sine-Gordon equation is obtained. Subsequently, the relation between the kinetic and potential energy of a fluxon is obtained along with the analytic relationships between the velocity of the fluxon and the dielectric thickness. Finally, an exact topological soliton solution is obtained for the sine-Gordon equation with and without strong perturbations through the use of the ansatz method.     

The window Josephson junction: a coupled linear nonlinear system

We investigate the interface coupling between the two-dimensional sine-Gordon equation and the two-dimensional wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effective one-dimensional model, and using soliton perturbation theory, compute the fixed points that can trap either a kink or antikink at an interface between two sine-Gordon media. This approximate analysis is validated by comparing with the solution of the partial differential equation and describes kink motion in the one-dimensional window junction. Using this, we analyze steady-state kink motion and derive values for the average speed in the one- and two-dimensional systems. Finally, we show how geometry and the coupling parameters can destabilize kink motion.     

Superconducting gates with fluxon logics

We have developed several logic gates (OR, XOR, AND and NAND) made of superconducting Josephson junctions. The gates based of the flux cloning phenomenon and high speed of fluxons moving in Josephson junctions of different shapes. In a contrast with previous design the gates operates extremely fast since fluxons are moving with the speed close to the speed of light. We have demonstrated their operations and indicated several ways to made a more complicated logic elements which have at the same time a compact form.     

Fluxons interactions in a Josephson junction with a phase-shift

We consider a long Josephson junction with a discontinuity point characterized by a gauge phase-shift. The system is described by a modified sine-Gordon equation. We study, in particular, the interactions between a fluxon and a fractional fluxon. A perturbation theory is developed in the small phase-shift limit to understand the characteristics of the interaction. Finally, numerical computations of the threshold bias current and the threshold velocity for a fluxon running over a fractional fluxon are presented.     

Effective boundary field theory for a Josephson junction chain with a weak link

We show that a finite Josephson junction (JJ) chain, ending with two bulk superconductors, and with a weak link at its center, may be regarded as a condensed matter realization of a two-boundary sine-Gordon model. Computing the partition function yields a remarkable analytic expression for the DC Josephson current as a function of the phase difference across the chain. We show that, in a suitable range of the chain parameters, there is a crossover of the DC Josephson current from a sinusoidal to a sawtooth behavior, which signals a transition from a regime where the boundary term is an irrelevant operator to a regime where it becomes relevant.     

Solitons in Josephson junctions: An overview

The dynamics of the Josephson tunnel junction is approximately described by a perturbed sine-Gordon equation. The Josephson tunnel junction is thus a convenient experimental solid state device for the study of solitons and solitonlike phenomena. The physical manifestation of the soliton is a propagating magnetic flux quantum ( ₀=h/2e=2.064×10^–15 V sec). Basic properties of the soliton and its relation to observable experimental quantities (zero field steps, microwave radiation, etc.) are reviewed. Recent direct measurements of the actual soliton profile are also mentioned.     

Spectroscopy of the fractional vortex eigenfrequency in a long Josephson 0-kappa junction

Fractional Josephson vortices carry a magnetic flux Phi, which is a fraction of the magnetic flux quantum Phi(0) approximately 2.07 x 10(-15) Wb. Their properties are very different from the properties of the usual integer fluxons. In particular, fractional vortices in 0-kappa Josephson junctions are pinned and have an oscillation eigenfrequency which is expected to be within the Josephson plasma gap. Using microwave spectroscopy, we investigate the dependence of the eigenfrequency of a fractional Josephson vortex on its magnetic flux Phi and on the bias current. The experimental results are in good agreement with the theory.     

Lifetime of the superconductive state in short and long Josephson junctions

We study the transient statistical properties of short and long Josephson junctions under the influence of thermal and correlated fluctuations. In particular, we investigate the lifetime of the superconductive metastable state finding the presence of noise induced phenomena. For short Josephson junctions we investigate the lifetime as a function both of the frequency of the current driving signal and the noise intensity and we find how these noise-induced effects are modified by the presence of a correlated noise source. For long Josephson junctions we integrate numerically the sine-Gordon equation calculating the lifetime as a function of the length of the junction both for inhomogeneous and homogeneous bias current distributions. We obtain a non-monotonic behavior of the lifetime as a function of the frequency of the current driving signal and the correlation time of the noise. Moreover we find two maxima in the non-monotonic behaviour of the mean escape time as a function of the correlated noise intensity.     

Shape changing and accelerating solitons in the integrable variable mass sine-gordon model

The sine-Gordon model with a variable mass (VMSG) appears in many physical systems, ranging from the current through a nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or perturbatively. We construct a class of VMSG models, integrable at both the classical and the quantum levels with exact soliton solutions, which can accelerate and change their shape, width, and amplitude simulating realistic inhomogeneous systems at certain limits.