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.     

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。     

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     

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.     

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.     

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.     

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.     

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.     

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.     

Interaction of rf field with a half-infinite Josephson junction

A standard sine-Gordon model of a half-infinite damped driven Josephson junction is considered, the external drive being accounted for by a boundary condition. For the case of a low-frequency ac drive we study oscillations of a fluxon pinned by the junction's edge and obtained an estimate for a range of values of the pinning energy where the driven oscillations are chaotic, which eventually implies chaotic depinning of the fluxon. For the case of the ac drive with a near-resonant frequency (i.e. close to the junction's plasma frequency) we find the wavenumber and amplitude of the driven plasma wave and the corresponding rate of energy absorption by the junction. The dependence of these quantities on the resonance frequency detuning proves to be hysteric. Finally, we consider the case when the external drive contains, on a level with near-resonant ac component, a dc one. We demonstrate that, the dc component being sufficiently large, the hysteresis disappears.     

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.     

Influence of a Magnetic Fluxon on the Vacuum Energy of Quantum Fields Confined by a Bag

We study the simultaneous influence of boundary conditions and external fields on quantum fluctuations by considering vacuum zero-point energies for quantum fields in the presence of a magnetic fluxon confined by a bag, circular and spherical for bosons and circular for fermions. The Casimir effect is calculated in a generalized cut-off regularization after applying zeta-function techniques to eigenmode sums and using recent techniques about Bessel zeta functions at negative arguments. Received: 25 March 1997 / Accepted: 3 September 1997     

Detection of interaural phase shift between a subaudible and an audible tone

Can a shift in interaural phase between a subthreshold signal and an audible contralateral probe tone affect perception of the probe? To obtain an answer, an 800-Hz tone was presented to both ears. The tone was presented continuously to one ear (-25 to + 10 dB SL) and in a sequence of four bursts per trial to the other ear (+ 10 dB SL). Interaural phase was reversed for either the second or the fourth burst in a 2 AFC task. Interaural phase-shift detection threshold (65% correct) varied with the intensity of the continuous signal; across subjects, this threshold varied from -21 to + 1 dB SL. When a 300-or 500-Hz masking tone was added to the ear with the continuous signal, phase-shift detection accuracy depended primarily upon the sensation level of the signal rather than its sound pressure level. These findings demonstrate temporal encoding at signal levels well below hearing threshold.     

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.     

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.     

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.     

Low-Energy Proton-Deuteron Scattering with a Coulomb-Modified Faddeev Equation

A modified version of the Faddeev three-body equation to accommodate the Coulomb interaction, which was used in the study of three-nucleon bound states, is applied to the proton-deuteron scattering problem at energies below the three-body breakup threshold. A formal derivation of the equation in a time-independent scattering theory is given. Numerical results for phase-shift parameters are presented to be compared with those of other methods and results of the phase-shift analysis. Differential cross sections and nucleon analyzing powers are calculated with the effects of three-nucleon forces, and these results are compared with recent experimental data. The difference between the nucleon analyzing power in proton-deuteron scattering and that in neutron-deuteron scattering is discussed.Received March 14, 2002; accepted September 29, 2002 Published online June 27, 2003     

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：     

Bifurcation,chaotic phenomena and control of chaos in a one—dimensional discrete Josephson lattice

We have investigated the fluxon dynamical behaviour in a one-dimensional parallel array of small Josephson junctions in the presence of an externally applied magnetic field. In the case of high damping,the system is in stable state. On the contrary, in the case of low damping, bifurcation and chaotic phenomena have been observed. Control of chaos is achieved by a delayed feedback mechanism, which drives the chaotic system into a selected unstable periodic orbit embadded within the associated strange attractor. It is attractive to control chaos to a periodic state, rather than operating always outside the device parameter space where chaos dominates.