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Topological phases in discrete-time quantum walks 

Andrea Alberti & Dieter Meschede


We propose to employ neutral atoms in optical lattices to experimentally investigate the topological properties underlying discrete-time quantum walks (DTQWs). Like in condensed matter physics, where insulators with nontrivial topological phases exist, DTQWs exhibit a rich topological structure. In particular, DTQWs represent an ideal model system to experimentally test novel topological phenomena recently predicted to occur in periodically driven systems (so-called Floquet systems): Periodic driving enriches the topological structure of these systems by endowing them with a new set of topological invariants. These new invariants play a key role to interpret phenomena that seem paradoxical within the theory established for static topological insulators.
Novel topological phases have been predicted for Floquet systems. We aim at unraveling the so-called bulk-boundary correspondence principle for Floquet topological insulators, which states that the number of topologically protected edge states is the algebraic difference of their adjacent Floquet topological invariants. We plan two approaches: direct observation of edge states at the boundary between two topological phases, and  classification of each individual topological phase in terms of its Floquet topological invariants.

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