Coordinate transformation in the model of long Josephson junctions: geometrically equivalent Josephson junctions

Semerdzhieva, E. G.; Boyadzhiev, T. L.; Shukrinov, Yu. M.

doi:10.1063/1.2128072

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…It is worth to point out that this Λ J variation stems from the variable junction width and cannot be modeled in terms of a spatially varying λ J in uniform-width JTL treated in Refs. ( [40], [41]); nevertheless, in the time independent case, it happens to be equivalent to a change in the J c of a uniform-width JTL [42]. Notably, the PDE of a confocal AJTJ does not differ from that of a circular one in Eq.…”

Section: Rotating Waves Along a Confocal Ajtjmentioning

confidence: 94%

Traveling electromagnetic waves in annular Josephson tunnel junctions

Monaco

2019

Wave Motion

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It is well known that long Josephson tunnel junctions (JTJs) act as active transmission lines for the slow-mode propagation of magnetic flux-quanta (in the form of solitary waves) that is at the base of many superconducting circuits. At the same time, they support the propagation of quasi-TEM dispersive waves with which the magnetic flux non-linearly interact. In this work, we study the properties of the electromagnetic resonances, under different conditions of practical interest, in annular JTJs (AJTJs), in which the wavelengths are limited to the length of the circumference divided by an integer. Our analysis is based on perturbed sine-Gordon equations the (1+1)-dimensional space with periodic boundary conditions. We discuss the discrete modes of the travelling EM waves in circular annular JTJs in the presence of an in-plane magnetic field, as well as in the recently introduced confocal annular JTJs (in the absence of magnetic field). In both cases, a variable-separation method leads to quantitatively different Mathieu equations characterized by even and odd spatially periodic solutions with different eigenfrequencies. It implicates that a single mode circulating wave is given by the superposition of two standing waves with the same wavelengths but different frequencies, and so has a periodically inverting direction of propagation. The control parameters of this frequency splitting are the in-plane magnetic field amplitude for the circular AJTJ and the aspect ratio for the confocal AJTJs. In the appropriate limits, the previously known solutions Email address: r.monaco@isasi.cnr.it and roberto.monaco@cnr.it (Roberto Monaco)

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Section: Rotating Waves Along a Confocal Ajtjmentioning

confidence: 94%

Traveling electromagnetic waves in annular Josephson tunnel junctions

Monaco

2019

Wave Motion

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“…It is worth to point out that this Λ J variation stems from the variable junction width and cannot be modeled in terms of a spatially varying λ J in uniform-width JTL treated in Refs. ( 39 , 40 ); nevertheless, in the time independent case, it happens to be equivalent to a change in the J c of a uniform-width JTL 41 .…”

Section: Theory Of One-dimensional Cajtjsmentioning

confidence: 99%

Engineering double-well potentials with variable-width annular Josephson tunnel junctions

Monaco

2016

J. Phys.: Condens. Matter

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Long Josephson tunnel junction are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system.

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“…Moreover, if an annular junction, also provided with a microshort, is considered, the vortex dynamics in a static magnetic field is modelled with the general perturbed sine-Gordon equation (see,f.i. [7]):…”

Section: Introductionmentioning

confidence: 99%

Filumena Marturano:

Angelis¹

Delirious Naples

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Coordinate transformation in the model of long Josephson junctions: geometrically equivalent Josephson junctions

Cited by 3 publications

References 16 publications

Traveling electromagnetic waves in annular Josephson tunnel junctions

Traveling electromagnetic waves in annular Josephson tunnel junctions

Engineering double-well potentials with variable-width annular Josephson tunnel junctions

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