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

TL;DR

This paper demonstrates that nonlinearities in a quantum walk can create an attractor-repeller pair of topological zero-modes, enabling control and trapping of the quantum walker at domain walls.

Contribution

It introduces a nonlinear quantum walk model where zero-modes form an attractor-repeller pair, allowing dynamical control of the walker at topological boundaries.

Findings

Zero-modes form an attractor-repeller pair due to nonlinearity.

Nonlinearities enable steering and trapping of the quantum walker.

Topological zero-modes can acquire a dynamical role in nonlinear quantum systems.

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.