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Observation of Topologically Protected Bound States in Photonic Quantum Walks

Takuya Kitagawa, Matthew A. Broome, Alessandro Fedrizzi, Mark Spencer Rudner, Erez Berg, Ivan Kassal, Alán Aspuru‐Guzik, Eugene Demler, Andrew G. White

Published Jan 1, 2011• 2 citations
Publisher

Abstract

Many emerging scientific developments are rooted in topology. We investigate one-dimensional topological phases in photonic quantum walks. We observe topologically protected bound states and reveal the existence of new topological phenomena unique to driven systems.
DOI
10.1364/iqec.2011.i750

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Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a time-periodic field. While there is ample theoretical work on topological phases of quantum walks where the coin operators are spin rotations, in experiments a different coin, the Hadamard operator, is often used instead. This was the case in a recent photonic quantum walk experiment, where protected edge states were observed between two bulks whose topological invariants, as calculated by the standard theory, were the same. This hints at a hidden topological invariant in the Hadamard quantum walk. We establish a relation between the Hadamard and the spin rotation operator, which allows us to apply the recently developed theory of topological phases of quantum walks to the one-dimensional Hadamard quantum walk. The topological invariants we derive account for the edge state observed in the experiment; we thus reveal the hidden topological invariant of the one-dimensional Hadamard quantum walk.