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Two-Dimensional Quantum Walk with Non-Hermitian Skin Effects |
Tianyu Li1, Yong-Sheng Zhang1,2*, and Wei Yi1,2* |
1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China 2CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
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Cite this article: |
Tianyu Li, Yong-Sheng Zhang, and Wei Yi 2021 Chin. Phys. Lett. 38 030301 |
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Abstract We construct a two-dimensional, discrete-time quantum walk, exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states is consistent with the Floquet winding number, calculated using a non-Bloch band theory, invoking time-dependent generalized Brillouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined via the local biorthogonal eigenwave functions of a non-unitary Floquet operator. Our work aims to stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.
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Received: 03 October 2020
Published: 02 March 2021
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PACS: |
03.65.Vf
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(Phases: geometric; dynamic or topological)
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67.85.-d
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(Ultracold gases, trapped gases)
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42.50.Gy
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(Effects of atomic coherence on propagation, absorption, and Amplification of light; electromagnetically induced transparency and Absorption)
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Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11974331, 11674306, and 61590932), and the National Key R&D Program (Grant Nos. 2016YFA0301700 and 2017YFA0304100). |
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