Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator

TL;DR

This paper explores how bound pairs of pi fluxons in a long Josephson junction with a ferromagnetic insulator exhibit relativistic time dilation effects, demonstrating internal oscillation frequency reductions analogous to time dilation.

Contribution

It introduces a double sine-Gordon model for fluxon dynamics with a ferromagnetic layer and shows relativistic time dilation of bound fluxon pairs' internal oscillations.

Findings

Bound pi fluxon pairs exhibit Lorentz-like frequency reduction.

Time dilation effect observed in fluxon internal oscillations.

Proposed experimental scheme for observing the effect.

Abstract

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.