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Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
| Title: | Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk |
| Authors: | Obuse, Hideaki Browse this author →KAKEN DB | | Asboth, Janos K. Browse this author | | Nishimura, Yuki Browse this author | | Kawakami, Norio Browse this author |
| Issue Date: | 23-Jul-2015 |
| Publisher: | American Physical Society |
| Journal Title: | Physical review B |
| Volume: | 92 |
| Issue: | 4 |
| Start Page: | 45424 |
| Publisher DOI: | 10.1103/PhysRevB.92.045424 |
| Abstract: | 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 |
| Type: | article |
| URI: | http://hdl.handle.net/2115/59768 |
| Appears in Collections: | 工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 小布施 秀明
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