Controlled dynamics of sine-Gordon breather in long Josephson junctions

A possible definition of the specific heat of open quantum systems is based on the reduced partition function of the system. For a free damped quantum particle, it has been found that under certain conditions, this specific heat can become negative at low temperatures. In contrast to the conventional approaches focusing on the system degree of freedom, here we concentrate on the changes induced in the environment when the system is coupled to it. Our analysis is carried out for an Ohmic environment consisting of harmonic oscillators and allows to identify the mechanism by which the specific heat becomes negative. Furthermore, the formal condition for the occurrence of a negative specific heat is given a physical interpretation in terms of the total mass of bath oscillators and the system mass.     

The current phase relation in Josephson tunnel junctions

The J(?) relation in SFIFS, SNINS, and SIS tunnel junctions is studied. A method for the analytical solution of linearized Usadel equations has been developed and applied to these structures. It is shown that the Josephson current across the structure has a sum of sin? and sin2? components. Two different physical mechanisms are responsible for the sign of sin2?. The first one is the depairing by current, which contributes positively to the sin2? term, while the second one is the finite transparency of SF or SN interfaces, which provides the negative contribution. In SFIFS junctions, where the first harmonic vanishes at the 0-π transition, the calculated second harmonic fully determines the J(?) curve.     

BCS quasi-particle tunnelling current in Josephson tunnel junctions

Summary The recent improvements in the fabrication technology have succeeded in obtaining high-quality Josephson tunnel junctions. TheI–V characteristics of these junctions exhibit now lesser and lesser differences from the theoretical predictions. The various figures of merit, so far introduced to qualify the junctions, appear now focused on too limited aspects and a direct comparison with the detailed prediction of the theory is in order. For this awaken interest in the detailed predictions of the BCS theory, we have revisited the relevant formulae for the quasi-particle tunnelling current. A detailed discussion of the analytical transformation necessary for a simple numerical evaluation of this current is reported. SeveralI–V curves are obtained using the parameter values corresponding to the case of Nb-based junctions, which is the actual running technology. Peculiar interesting aspects are outlined.     

Approximate treatment of two soliton solutions of the sine-Gordon equation

The so called breather solution of the sine-Gordon equation is phenomenologically described by an appropriately choosen potential acting between two particles. For some applications the method proves to be equivalent to other classical and quantum calculations.     

Calculations of the Josephson current distribution in two-dimensional tunnel junctions

A numerical method has been developed for the calculation of the time-independent Josephson current distribution in two-dimensional tunnel junctions. Results obtained with this method agree well with experimental measurements of the Josephson current distribution using low temperature scanning electron microscopy.     

双层结构铁磁-超导隧道结的直流Josephson电流

通过求解Bogoliubov_de Gennes(BdG)方程得到铁磁超导共存态(FS)的自洽方程，在考虑结 界面的粗糙情形下，由推广的Furusaki_Tsukada(FT)的电流公式计算了铁磁超导态/ 绝缘层 / 铁磁超导态(FS/I/FS)结的直流Josephson电流，讨论了FS/I/FS结的直流Josephson临界 电流随磁交换能、温度的变化情况.研究表明：当结界面势垒散射强度和粗糙势垒散射强度 比较弱时磁交换能总是抑制FS/I/FS结的直流Josephson临界电流，而当结左右两边FS中铁 关键词： FS/I/FS超导隧道结 铁磁超导共存态 直流Josephson电流 粗糙势垒散射     

Anomalous rf induced steps in long resonant Josephson tunnel junctions

Anomalous phase locked current steps are experimentally observed in the I–V characteristic of a long Josephson tunnel junction driven by microwaves at the frequency of its geometrical resonance.     

Thickness dependence of the maximum DC Josephson current in superconducting proximity junctions

We investigated the maximum dc Josephson current I_M in NbNb_xO_yCu/Pb junctions as a function of normal layer thickness d_Cu. Theoretical calculations based on the McMillan proximity effect model are in good agreement with the experimental data. The monotonous decrease of RI_M (R is the normal tunneling resistance) indicates the absence of any oscillatory behaviour or anomaly in the pair amplitude F_Cu(d_Cu) of the Cu/Pb sandwich, in contradiction with theoretical prediction.     

Quasi-periodic solutions of the sine-Gordon equation

Two-phase quasi-periodic solutions of the sine-Gordon equation are discussed. It is shown that the solutions expressed by the multidimensional θ-function form a broader class than the well-known factorised solutions 4 arctan [f(u)g(v)]. Expressions describing the spatial and temporal period are also given.     

Mixed solutions of the sine-Gordon equation

The aim of this note is to present an explicit formula for the mixed solution of the sine-Gordon equation, i.e. the solution describing a multisoliton process on a background of multiphase quasi-periodic process.     

Anomalous Josephson vortex solutions in Josephson junctions with multiple tunneling channels

We construct a theory for Josephson junction with multiple tunneling channels. We focus on two situations, i.e., a heterotic junction composed of two-gap-superconductor, insulator, and one-gap-superconductor, and a grain-boundary junction formed by two identical multi-gap superconductors. Then, we show that the magnetic field distribution of the Josephson vortex for ±s-wave superconductivity is much more enlarged than that for s-wave without sign change between the order parameters. We display such anomalous vortices and suggest how to evaluate the enlargement.     

The solutions of the two-dimensional sine-Gordon equation

Three-parameter families of the solutions of sine-Gordon equation in two dimensions are presented.     

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.     

Josephson coupling and Fiske dynamics in ferromagnetic tunnel junctions

We report on the fabrication of Nb/AlO _x /Pd_0.82Ni_0.18/Nb superconductor/insulator/ferromagnetic metal/superconductor (SIFS) Josephson junctions with high critical current densities, large normal resistance times area products, high quality factors, and very good spatial uniformity. For these junctions a transition from 0- to π-coupling is observed for a thickness d _F @\simeq 6 nm of the ferromagnetic Pd_0.82Ni_0.18 interlayer. The magnetic field dependence of the π-coupled junctions demonstrates good spatial homogeneity of the tunneling barrier and ferromagnetic interlayer. Magnetic characterization shows that the Pd_0.82Ni_0.18 has an out-of-plane anisotropy and large saturation magnetization, indicating negligible dead layers at the interfaces. A careful analysis of Fiske modes provides information on the junction quality factor and the relevant damping mechanisms up to about 400 GHz. Whereas losses due to quasiparticle tunneling dominate at low frequencies, the damping is dominated by the finite surface resistance of the junction electrodes at high frequencies. High quality factors of up to 30 around 200 GHz have been achieved. Our analysis shows that the fabricated junctions are promising for applications in superconducting quantum circuits or quantum tunneling experiments.     

Magnetic field behavior of resonant current steps in one dimensional arrays of Josephson tunnel junctions

We study the magnetic field behavior of the resonant current steps appearing in one dimensional arrays of Josephson tunnel junctions. The analysis is carried out in the framework of the Kulik theory of resonances in small Josephson junctions, and the theoretical maximum current amplitude of the Fiske steps is computed as a function of the applied magnetic field. Preliminary measurements of the Fiske step current modulations induced by varying the magnetic field is also reported and discussed.     

Solitions and separable elliptic solutions of the sine-Gordon equation

We point out that the two-soliton (antisoliton) solutions of the sine-Gordon equation may be obtained as limiting cases of a separable, two-parameter family of elliptic solutions. The solitons are found on the boundary of the parameter space for the elliptic solutions when the latter are considered over their usual complex domain.     

Inelastic tunnelling and the pair-quasiparticle interference current in Josephson junctions

The contribution to the quasiparticle current and pair—quasiparticle interference current of inelastic tunnelling due to the excitation of a boson mode in the tunnelling barrier is evaluated.     

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.     

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.