Long Josephson junctions with spatially inhomogeneous driving

The phase dynamics of a long Josephson junction with spatially inhomogeneously distributed bias current is considered for the case of a dense soliton chain (regime of the Flux Flow oscillator). To derive the analytical solution of the corresponding sine-Gordon equation the Poincare method has been used. In the range of the validity of the theory good coincidence between analytically derived and numerically computed current-voltage characteristics have been demonstrated for the simplest example of unitstep function distribution of bias current (unbiased tail). It is shown, that for the considered example of bias current distribution, there is an optimal length of unbiased tail that maximizes the amplitude of the main harmonic and minimizes the dynamical resistance (thus leading to reduction of a linewidth).Comment: 7 pages, 5 figure

Josephson Tunnel Junctions in a Magnetic Field Gradient

We measured the magnetic field dependence of the critical current of high quality Nb-based planar Josephson tunnel junctions in the presence of a controllable non-uniform field distribution. We found skewed and slowly changing magnetic diffraction patterns quite dissimilar from the Fraunhofer-like ones typical of a homogeneous field. Our findings can be well interpreted in terms of recent theoretical predictions [R. Monaco, J. Appl. Phys. vol.108, 033906 (2010)] for a uniform magnetic field gradient leading to Fresnel-like magnetic diffraction patterns. We also show that Fiske resonances can be suppressed by an asymmetric magnetic field profile.Comment: 8 pages, 4 figure

Josephson Vortex Qubit based on a Confocal Annular Josephson Junction

We report theoretical and experimental work on the development of a Josephson vortex qubit based on a confocal annular Josephson tunnel junction (CAJTJ). The key ingredient of this geometrical configuration is a periodically variable width that generates a spatial vortex potential with bistable states. This intrinsic vortex potential can be tuned by an externally applied magnetic field and tilted by a bias current. The two-state system is accurately modeled by a one-dimensional sine-Gordon like equation by means of which one can numerically calculate both the magnetic field needed to set the vortex in a given state as well as the vortex depinning currents. Experimental data taken at 4.2K on high-quality Nb/Al-AlOx/Nb CAJTJs with an individual trapped fluxon advocate the presence of a robust and finely tunable double-well potential for which reliable manipulation of the vortex state has been classically demonstrated. The vortex is prepared in a given potential by means of an externally applied magnetic field, while the state readout is accomplished by measuring the vortex-depinning current in a small magnetic field. Our proof of principle experiment convincingly demonstrates that the proposed vortex qubit based on CAJTJs is robust and workable.Comment: 20 pages, 11 figure

Field Cooled Annular Josephson Tunnel Junctions

We investigate the physics of planar annular Josephson tunnel junctions quenched through their transition temperature in the presence of an external magnetic field. Experiments carried out with long Nb/Al-AlOx/Nb annular junctions showed that the magnetic flux trapped in the high-quality doubly-connected superconducting electrodes forming the junction generates a persistent current whose associated magnetic field affects the both the static and dynamics properties of the junctions. More specifically, the field trapped in the hole of one electrode combined with a d.c. bias current induces a viscous flow of dense trains of Josephson vortices which manifests itself through the sequential appearance of displaced linear slopes, Fiske step staircases and Eck steps in the junction's current-voltage characteristic. Furthermore, a field shift is observed in the first lobe of the magnetic diffraction pattern. The effects of the persistent current can be mitigated or even canceled by an external magnetic field perpendicular to the junction plane. The radial field associated with the persistent current can be accurately modeled with the classical phenomenological sine-Gordon model for extended one-dimensional Josephson junctions. Extensive numerical simulations were carried out to disclose the basic flux-flow mechanism responsible for the appearance of the magnetically induced steps and to elucidate the role of geometrical parameters. It was found that the imprint of the field cooling is enhanced in confocal annular junctions which are the natural generalization of the well studied circular annular junctions.Comment: 26 pages, 10 figures. Supercond. Sci. Technol (2020

Flux Flow Effects in Annular Josephson Tunnel Junctions

We investigate Josephson flux-flow in annular Josephson tunnel junctions (AJTJs) under the application of magnetic fields generating finite-voltage steps in their current-voltage characteristics. Experimental data are presented for confocal AJTJs which are the natural generalization of the well studied circular AJTJs for which flux flow effects have never been reported. Displaced linear slopes, Fiske step staircases and Eck steps were sequentially recorded at $4.2\,K$ with high-quality Nb/Al-AlOx/Nb confocal AJTJs when increasing the strength of a uniform magnetic field applied in the plane of the junction. Their amplitude was found to strongly depend not only on the strength, but also on the orientation, of the external field. Extensive numerical simulations based on a phenomenological sine-Gordon model developed for confocal AJTJs were carried out to disclose the basic flux-flow mechanism responsible for the appearance of magnetically induced steps and to elucidate the role of several critical parameters, namely, the field orientation, the system loss and the annulus eccentricity. It was found that in a topologically closed system, such as the AJTJ, where the number of trapped fluxons is conserved and new fluxons can be created only in the form of fluxon-antifluxon pairs, the existence of a steady viscous flow of Josephson vortices only relies on the capability of the fluxons and antifluxons to be generated and to annihilate each other inside the junction. This also implies that flux-flow effects are not observable in circular AJTJs.Comment: 26 pages, 8 figure

Form and width of spectral line of Josephson Flux-Flow oscillator

The behavior of a Josephson flux-flow oscillator in the presence of both bias current and magnetic field fluctuations has been studied. To derive the equation for slow phase dynamics in the limit of small noise intensity the Poincare method has been used. Both the form of spectral line and the linewidth of the flux-flow oscillator have been derived exactly on the basis of technique presented in the book of Malakhov, known limiting cases are considered, limits of their applicability are discussed and appearance of excess noise is explained. Good coincidence of theoretical description with experimental results has been demonstrated.Comment: 10 pages, 5 figure

A quantitative investigation of the effect of a close-fitting superconducting shield on the coil-factor of a solenoid

Superconducting shields are commonly used to suppress external magnetic interference. We show, that an error of almost an order of magnitude can occur in the coil-factor in realistic configurations of the solenoid and the shield. The reason is that the coil-factor is determined by not only the geometry of the solenoid, but also the nearby magnetic environment. This has important consequences for many cryogenic experiments involving magnetic fields such as the determination of the parameters of Josephson junctions, as well as other superconducting devices. It is proposed to solve the problem by inserting a thin sheet of high-permeability material, and the result numerically tested.Comment: 3 pages, 4 figures, submitted to AP