Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk

Abstract

The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero-modes) at boundaries or domain walls. Here we show that a topological zero-mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero-modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero-modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.

4 pages, 5 figures

References in corpus (9)

• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Exploring Topological Phases With Quantum Walks
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Topological Transition in a Non-Hermitian Quantum Walk
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Asymptotic evolution of quantum walks with random coin
• Nonlinear optical Galton board
• Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons
• Localisation, delocalisation, and topological transitions in disordered 2D quantum walks

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• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Asymptotic stability of small bound state of nonlinear quantum walks
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• Non-Linear Interference Challenging Topological Protection of Chiral Edge States
• Scattering and inverse scattering for nonlinear quantum walks