Compact stationary fluxons in the Josephson junction ladder

TL;DR

This paper demonstrates the existence of exact stationary compact fluxon solutions in Josephson junction ladders, highlighting their unique properties and conditions for stability, which differ from parallel arrays.

Contribution

It introduces the concept of exact compact fluxon solutions in Josephson junction ladders, contrasting with their absence in parallel arrays, and explores their properties under various conditions.

Findings

Compact fluxons are exact solutions in Josephson junction ladders.

Anti-symmetric states have zero energy with even topological charge.

External magnetic fields inhibit the existence of compact states.

Abstract

Stationary compact fluxon profiles are shown to be exact solutions of the inductively coupled and dc-biased Josephson junction ladder. Such states do not exist in the parallel Josephson junction array which is described by the standard discrete sine-Gordon equation. It is shown that there are compact fluxon and multi-fluxon states which either satisfy the top-bottom antisymmetry or are asymmetric. The anti-symmetric states have zero energy if their topological charge is even and the asymmetric states always have zero energy. Depending on the anisotropy constant the compact fluxons can either coexist with the non-compact states or only compact states are possible. External magnetic field prevents compact state existence.