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.     

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.     

Bifurcations of soliton bound states in nonuniform Josephson junctions

Bifurcations of soliton (fluxon) bound states in long Josephson junctions with local attractive inhomogeneities are analysed. A simple criterion for stability of the these bound states is proposed. A possibility of a direct experimental observation of the bound states and of their bifurcations depending on an external magnetic field and/or positions of inhomogeneities is pointed out.     

Radiation linewidth of a long Josephson junction in the flux-flow regime

Theoretical model for the radiation linewidth in a multi-fluxon state of a long Josephson junction is presented. Starting from the perturbed sine-Gordon model with the temperature dependent noise term, we use a collective coordinate approach in order to calculate the finite radiation linewidth due to the internal degrees of freedom in the moving fluxon chain. At low fluxon density, the radiation linewidth is expected to be substantially larger than that of a lumped Josephson oscillator. With increasing the fluxon density, a crossover to a much smaller linewidth approaching the lumped oscillator limit is predicted.     

Fluxon pinning on a periodical structure of magnetic inclusions in a Josephson contact

The low speed motion of a fluxon in a Josephson contact containing a periodical system of magnetic inclusions is considered. The existence of fluxon pinning at some distance from the magnetic inclusion is shown. This distance depends both on the structure period and on the parameters of the magnetic inclusions. The critical current of fluxon depinning is obtained. The existence of two different types of critical current is shown: the main critical current of the fluxon leaving the inclusion and a small critical current of the fluxon jumping between neighbouring potential minima.     

Reflection of fluxons on a Josephson line cavity

A single fluxon on a semi-infinite Josephson line is reflected at a passive or an active termination. By numerical computation we find a single reflected fluxon, an antifluxon, absorption of the incident fluxon, or fission into an arbitrary number of fluxons depending on the boundary condition. For the passive termination an analytical approximation based on energy analysis is developed.     

High-efficiency deterministic Josephson vortex ratchet

We investigate experimentally a Josephson vortex ratchet--a fluxon in an asymmetric periodic potential driven by a deterministic force with zero time average. The highly asymmetric periodic potential is created in an underdamped annular long Josephson junction by means of a current injector providing an efficiency of the device up to 91%. We measured the ratchet effect for driving forces with different spectral content. For monochromatic high-frequency drive the rectified voltage becomes quantized. At high driving frequencies we also observe chaos, subharmonic dynamics, and voltage reversal due to the inertial mass of a fluxon.     

Stochastic dynamics of a Josephson fluxon in an inhomogeneous junction

A study is made of fluxon motion in a long Josephson junction with a local inhomogeneity (microresistor) in the presence of an alternating external current. Nonlinear resonances in the fluxon dynamics are considered. The process by which a fluxon trapped at an inhomogeneity is stochastically depinned under the influence of a periodic current is investigated analytically and numerically. Zh. Tekh. Fiz. 67, 57–61 (August 1997)     

Josephson结中激发孤子的电流脉冲方法──原理与数值实验

根据反散射理论讨论了电流脉冲法产生磁通孤子的阈值条件。对甚长结作的数值实验与理论符合很好。对有限结，考虑到边界效应，电流台阶范围等因素，对孤子激发条件有额外的要求，对圆对称环域结用脉冲法激发了孤子，并分析了其中回波效应、外磁场等对激发条件的影响。所有结果表明，电流脉冲法是在Ｊｏｓｅｐｈｓｏｎ结中激发孤子态的有效方法，理论阈值条件可以提供有益的参考作用。     

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.     

Interaction between a BSCCO-type intrinsic Josephson junction and a microwave cavity

The electrical behavior of anisotropic BSCCO single crystals is modeled by mutually coupled long Josephson junctions. We show that although the fluxons in the different layers do not a priori prefer the in-phase motion desired for many potential applications it is possible to induce such behavior by coupling the system to a high-Q resonator with a resonance frequency corresponding to fluxon in-phase motion. The resulting model is a set of coupled non-linear partial differential equations. By direct numerical simulations we have demonstrated that the qualitative behavior of the combined stacked long Josephson junctions and cavity system can be understood on the basis of the general concepts of nonlinear oscillators interacting with a resonator. For some region of the parameter space it is possible to reach the desired synchronous state, making the system potentially suitable for applications. We also look at the different dynamical states defined by different fluxon dynamical states in combination with different cavity properties.     

Parametric resonance in the system of long Josephson junctions

The phase dynamics of the system of long Josephson junctions whose length exceeds the Josephson penetration depth has been studied. The possibility of the appearance of a longitudinal plasma wave and parametric resonance has been demonstrated. Both inductive and capacitive couplings between Josephson junctions have been taken into account in the calculations. The current-voltage characteristics, as well as time evolution of the spatial distribution of the electric charge in superconducting layers and the magnetic field, have been calculated in all Josephson junctions of the system. The coexistence of the longitudinal plasma wave and fluxon states has been observed in the region of parametric resonance beginning with a certain length of the Josephson junction. This indicates the appearance of a new unique collective excitation in the system of coupled Josephson junctions, namely, a composite state of the Josephson current, electric field, and vortex magnetic field.     

Fluxon interaction with the finite-size dipole impurity

Interaction of the fluxon with the finite size dipole impurity in the long Josephson junction is investigated. The impurity has polarity and will be referred to as a dipole impurity because it also has a direction and, consequently, changes its sign under the space inversion transform $x\to ?x$. Such a model is used to describe the inductively coupled to the Josephson transmission line qubit and the misaligned Abrikosov vortex that penetrates into the long Josephson junction. We derive the approximate equations of motion for the fluxon centre of mass and its velocity. With the help of these equations we demonstrate that pinning and scattering of the fluxon on the impurity differs significantly from the case of the point impurity which is modelled by the derivative of the Dirac's δ-function.     

Ratchetlike dynamics of fluxons in annular Josephson junctions driven by biharmonic microwave fields

Experimental observation of the unidirectional motion of a topological soliton driven by a biharmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The dependence of the fluxon mean velocity at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.     

Fluxon dynamics on the circular Josephson oscillator

A hamiltonian perturbation theory is developed for the perturbed sine-Gordon equation with periodic boundary conditions modelling the Josephson ring oscillator. Stationary fluxon velocities are determined as function of length, loss and bias parameters.     

Nonlinear resonance between a soliton and Josephson plasma waves: experiment and theory

Resonant interaction of a soliton (Josephson fluxon) with its self-generated Josephson plasma waves is studied experimentally, numerically, and analytically. An externally applied magnetic field H forms a cos-like potential relief for the soliton in the annular junction. Soliton motion under the influence of the bias current leads to an emission of plasma waves, which gives rise to a resonance at a certain soliton velocity. This resonance on the current–voltage characteristics shows a clear backbending accompanied by a negative differential resistance. Our analysis quantitatively explains the observed effect.     

Ratchet effect: demonstration of a relativistic fluxon diode

We report the observation of the ratchet effect for a relativistic flux quantum trapped in an annular Josephson junction embedded in an inhomogeneous magnetic field. In such a solid state system, mechanical quantities are proportional to electrical quantities, so that the ratchet effect represents the realization of a relativistic-flux-quantum-based diode. Mean static voltage response, equivalent to directed fluxon motion, is experimentally demonstrated in such a diode for deterministic as well as stochastic oscillating current forcing.     

层状耦合约瑟夫森双结中的孤子解

基于Sakai-Bodin-Petersen理论，我们求解了对称的双约瑟夫森结的耦合非线性方程组．结果表明，线性化方程组的同相和反相解所对应的两种磁通运动模式也存在于原始的非线性方程组的解中，同时非线性方程组独有的位相锁定的扭折（kinks）形式的磁通运动在低能情况下会演化为孤子解．     

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.     

Frequency divider by underdamped Josephson transmission line

A parallel array of coupled short Josephson junctions under boundary ac driving is theoretically investigated. The driving response is monitored via numerical simulations on the associated Frenkel-Kontorova model as an oscillating output current at the other boundary junction. The theoretical analysis is conducted assuming the phase locking of boundary driving with exact stationary solution of sine-Gordon equation that can be represented by a kink (fluxon) motion back and forth in the restricted geometry of the array. As a consequence the results suggest the conception of a device which could switch to the conducting regime not according to intensity range but rather to given (quantized) frequency range. Moreover our findings indicate also a frequency converting scenario by choosing appropriately the system length and injected fluxon number.