Synchronization of One Dimensional Array of Point Josephson Junctions Coupled to a Common Load

TL;DR

This paper investigates the synchronization phenomena in a one-dimensional array of Josephson junctions coupled via a common capacitor, analyzing stability, effects of thermal noise, and dynamic relaxation behaviors.

Contribution

It provides a comprehensive stability diagram and explores the effects of noise, dissipation, and shunt capacitance on synchronization in Josephson junction arrays.

Findings

Synchronization stability depends on shunt parameters and dissipation.

Thermal noise causes a phase transition leading to desynchronization.

Relaxation time increases with system size and temperature, decreases with shunt capacitance.

Abstract

We study the synchronization in a one dimensional array of point Josephson junctions coupled to a common capacitor, which establishes a long-range interaction between junctions and synchronizes them. The stability diagram of synchronization in a noise-free system is obtained. The current when junctions transform from resistive state into superconducting state, is then calculated and its dependence on the shunt parameters and the dissipation of junctions is revealed. In the presence of thermal noise, the synchronized oscillations are destroyed at a critical temperature and the system undergoes a continuous phase transition of desynchronization. A possible stability diagram of the synchronized oscillations with respect to thermal noise, current, dissipations and shunt capacitance is then constructed. Finally we investigate the dynamic relaxation from random oscillations into synchronized state. The relaxation time increases with the system size and temperature, but is reduced by the shunt capacitor.