Nonlinear dynamical topological phases in Cooper-pair box array

TL;DR

This paper introduces a nonlinear dynamical topological phase transition in a Cooper-pair box array, where topological properties are revealed through quench dynamics rather than static measurements.

Contribution

It proposes a system where topological phases are identified via dynamics, specifically through quench-induced wave propagation in a nonlinear superconducting array.

Findings

Revealed a rich topological phase diagram via quench dynamics.

Demonstrated topological properties are only observable through system dynamics.

Connected nonlinear differential equations describe the system's behavior.

Abstract

The topological property of a system is a static property in general. For instance, the topological edge state is observed by measuring the local density of states. In this work we propose a system whose topological property is only revealed by dynamics. As a concrete example, we explore a nonlinear dynamical topological phase transition revealed by a quench dynamics of a Cooper-pair box array connected with capacitors. It is described by coupled nonlinear differential equations due to the Josephson effect. It is trivial as far as the static system is concerned. However, the wave propagation induced by the quench dynamics demonstrates a rich topological phase diagram in terms of the strength of the input.