Topological bound states of a quantum walk with cold atoms

Abstract

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically non-trivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

17 pages, 16 figures

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• Measuring Chern numbers in Hofstadter strips
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• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
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• Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion