Dynamics of An Underdamped Josephson Junction Ladder

TL;DR

This paper analytically reduces the complex dynamics of an underdamped Josephson junction ladder to a discrete sine-Gordon model and confirms key behaviors through numerical simulations, revealing flux flow, whirling regimes, and voltage steps.

Contribution

It introduces an approximate reduction of the Josephson ladder dynamics to the discrete sine-Gordon equation and validates it with numerical solutions, providing insights into fluxon behavior and voltage characteristics.

Findings

Discrete sine-Gordon-like IV characteristics observed

Flux flow and whirling regimes identified

Voltage steps predicted and confirmed numerically

Abstract

We show analytically that the dynamical equations for an underdamped ladder of coupled small Josephson junctions can be approximately reduced to the discrete sine-Gordon equation. As numerical confirmation, we solve the coupled Josephson equations for such a ladder in a magnetic field. We obtain discrete-sine-Gordon-like IV characteristics, including a flux flow and a ``whirling'' regime at low and high currents, and voltage steps which represent a lock-in between the vortex motion and linear ``phasons'', and which are quantitatively predicted by a simple formula. At sufficiently high anisotropy, the fluxons on the steps propagate ballistically.