Single fluxon in double stacked Josephson junctions: Analytic solution

TL;DR

This paper derives an approximate analytic solution for a single fluxon in double stacked Josephson junctions, revealing complex behavior including an inverted magnetic field and providing a comparison with numerical simulations.

Contribution

It introduces a novel analytic approach for fluxons in double SJJ's, accounting for arbitrary parameters and coupling, with second order corrections and validation against simulations.

Findings

Fluxon characterized by two components with different velocities and depths.

Analytic solutions show good agreement with numerical simulations.

Fluxons can exhibit an inverted magnetic field near certain velocities.

Abstract

We derive an approximate analytic solution for a single fluxon in a double stacked Josephson junctions (SJJ's) for arbitrary junction parameters and coupling strengths. It is shown that the fluxon in a double SJJ's can be characterized by two components, with different Swihart velocities and Josephson penetration depths. Using the perturbation theory we find the second order correction to the solution and analyze its accuracy. Comparison with direct numerical simulations shows a quantitative agreement between exact and approximate analytic solutions. It is shown that due to the presence of two components, the fluxon in SJJ's may have an unusual shape with an inverted magnetic field in the second junction when the velocity of the fluxon is approaching the lower Swihart velocity.