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Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk

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タイトル: Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
著者: Obuse, Hideaki 著作を一覧する
Asboth, Janos K. 著作を一覧する
Nishimura, Yuki 著作を一覧する
Kawakami, Norio 著作を一覧する
発行日: 2015年 7月23日
出版者: American Physical Society
誌名: Physical review B
巻: 92
号: 4
開始ページ: 45424
出版社 DOI: 10.1103/PhysRevB.92.045424
抄録: 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.
Rights: ©2015 American Physical Society
資料タイプ: article
URI: http://hdl.handle.net/2115/59768
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 小布施 秀明

 

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