Attractor-repeller pair of topological zero modes in a nonlinear quantum walk
Yevhen Gerasimenko, Brian Tarasinski, C. W. J. Beenakker · Physical Review A · 2016
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.