Shape waves in 2D Josephson junctions: exact solutions and time dilation

TL;DR

This paper introduces a new class of shape-preserving excitations in 2D Josephson junctions, acting as a relativistic clock for vortex dynamics, with potential experimental verification of time dilation effects.

Contribution

It provides exact solutions for shape waves in Josephson vortices and explores their role as a relativistic clock, advancing understanding of vortex dynamics in superconducting systems.

Findings

Derived universal analytical expression for excitation energy.

Identified conditions for creating shape excitations.

Proposed experiment to observe relativistic time dilation in vortex motion.

Abstract

We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically-moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity.