Charge Solitons in 1-D Arrays of Serially Coupled Josephson Junctions

TL;DR

This paper investigates charge solitons in a one-dimensional array of Josephson junctions with dominant kinetic inductance, analyzing their classical and quantum dynamics, and exploring potential macroscopic quantum phenomena such as persistent currents.

Contribution

It introduces a continuum sine-Gordon model for charge solitons in Josephson arrays with large kinetic inductance, and discusses their classical and quantum behaviors including potential macroscopic quantum effects.

Findings

Charge solitons exhibit relativistic motion leading to saturation in I-V characteristics.

Quantum charge solitons can sustain persistent currents if dephasing length exceeds array circumference.

Charge solitons are macroscopic quantum objects with a width of about 100 microns.

Abstract

We study a 1-D array of Josephson coupled superconducting grains with kinetic inductance which dominates over the Josephson inductance. In this limit the dynamics of excess Cooper pairs in the array is described in terms of charge solitons, created by polarization of the grains. We analyze the dynamics of these topological excitations, which are dual to the fluxons in a long Josephson junction, using the continuum sine-Gordon model. We find that their classical relativistic motion leads to saturation branches in the I-V characteristic of the array. We then discuss the semi-classical quantization of the charge soliton, and show that it is consistent with the large kinetic inductance of the array. We study the dynamics of a quantum charge soliton in a ring-shaped array biased by an external flux through its center. If the dephasing length of the quantum charge soliton is larger than the circumference of the array, quantum phenomena like persistent current and coherent current oscillations are expected. As the characteristic width of the charge soliton is of the order of 100 microns, it is a macroscopic quantum object. We discuss the dephasing mechanisms which can suppress the quantum behaviour of the charge soliton.