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The topological property of a system is a static property in general. Forinstance, the topological edge state is observed by measuring the local densityof states. In this work we propose a system whose topological property is onlyrevealed by dynamics. As a concrete example, we explore a nonlinear dynamicaltopological phase transition revealed by a quench dynamics of a Cooper-pair boxarray connected with capacitors. It is described by coupled nonlineardifferential equations due to the Josephson effect. It is trivial as far as thestatic system is concerned. However, the wave propagation induced by the quenchdynamics demonstrates a rich topological phase diagram in terms of the strengthof the input.

Nonlinear dynamical topological phases in Cooper-pair box array