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.     

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.     

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.     

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.     

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)     

Fluxon ratchet potentials in superconducting circuits

A fluxon in a Josephson-junction parallel array behaves like a single particle in a periodic pinning potential. Different configurations of critical currents and cell areas result in different profiles for the fluxon potential. We analyze the minimal conditions to achieve an effective potential in which mirror symmetry is absent, namely a fluxon ratchet potential. Following one of the configurations, we designed circular arrays and probed some of the fluxon properties. Theoretical predictions are nicely fulfilled by the experiments. Received: 20 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

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.     

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.     

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。     

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.     

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.     

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.     

Josephson磁通孤子振荡器中热噪声研究

研究了可作为微波振荡器的长Sosephson隧道结中的磁通孤子在有限温度下受热噪声影响的运动。当Josephson隧道结被偏置在零场台阶状态,热噪声使孤子的运动速度在平均值附近涨落,孤子的平均速度对应于隧道结的平均电压,也对应于对外辐射电磁波的平均频率,速度的涨落对应于辐射一有限的频带宽度。研究表明,隧道结典型辐射频率为10GHZ,在液氦温区其频带宽约为1KHZ,是很窄的。热噪声同时也激发了一些连续模。用反散射方法的微扰论讨论了每模式的平均能量为k_BT,而孤子在低速极限的平均动能为1 关键词：     

Classical analog to topological nonlocal quantum interference effects

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and nonlocality-local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and nonlocal features of the Aharonov-Bohm effect can be manifested in a classical model that incorporates random noise. The model also suggests new types of multiparticle topological nonlocal effects which have no quantum analog.     

Directed transport of a Brownian particle in a periodically tapered tube

The problem of the motion of a Brownian particle in a periodically tapered tube induced by a time-periodic longitudinal force with zero mean is considered. Under the action of this force, the particle is shown to drift in a direction opposite to the constant load force applied to it. Analytical solutions for the drift velocity, the stopping force (the load causing the effect to disappear), and the efficiency of converting the energy introduced by perturbations into directed motion have been obtained at a large amplitude of the driving force, when the effect being discussed is maximal. In the range of its applicability extending from zero to asymptotically large force switching frequencies (proportional to the amplitude of the driving force), these solutions are in good agreement with the results of Brownian dynamics simulations.     

Effective classical stochastic theory for quantum tunneling

The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.     

Current-voltage characteristics of extended Josephson junctions with viscous magnetic-flux transport

A theory that describes the current-voltage characteristics of extended Josephson junctions is built. The width of the junctions is much larger than the mean free path of a single fluxon, with the length of the path determined by energy dissipation in the junction. Explicit analytic expressions are derived for the maximum supercurrent in the junction and the low-voltage asymptotic behavior of the current-voltage characteristics. Zh. éksp. Teor. Fiz. 112, 910–925 (September 1997)     

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．     

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.     

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.