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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: |
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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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| [1] | Carmichael H J 1993 Phys. Rev. Lett. 70 2273 |
| [2] | Lee T E 2016 Phys. Rev. Lett. 116 133903 |
| [3] | Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808 |
| [4] | McDonald A, Pereg-Barnea T and Clerk A A 2018 Phys. Rev. X 8 041031 |
| [5] | Borgnia D S, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802 |
| [6] | Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803 |
| [7] | Yao S, Song F and Wang Z 2018 Phys. Rev. Lett. 121 136802 |
| [8] | Yokomizo K and Murakami S 2019 Phys. Rev. Lett. 123 066404 |
| [9] | Yang Z S, Zhang K, Fang C and Hu J P 2020 Phys. Rev. Lett. 125 226402 |
| [10] | Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402 |
| [11] | Martinze Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401(R) |
| [12] | Zhang X Z and Gong J B 2020 Phys. Rev. B 101 045415 |
| [13] | Zeng Q B, Yang Y B and Xu Y 2020 Phys. Rev. B 101 020201(R) |
| [14] | Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801 |
| [15] | Wang X R, Guo C X and Kou S P 2020 Phys. Rev. B 101 121116(R) |
| [16] | Lee C H and Thomale R 2019 Phys. Rev. B 99 201103(R) |
| [17] | Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 170401 |
| [18] | Helbig T, Hofmann T, Imhof S, Abdelghany M, Klessling T, Molenkamp L W, Lee C H, Szameit A, Greiter M and Thomale R 2020 Nat. Phys. 16 747 |
| [19] | Hofmann T, Helbig T, Schindler F, Salgo N, Brzezińska M, Greiter M, Kiessling T, Wolf D, Vollhardt A, Kabaši A, Lee C H, Bilušić A, Thomale R and Neupert T 2020 Phys. Rev. Res. 2 023265 |
| [20] | Ghatak A, Brandenbourger M, van Wezel J and Coulais C 2020 Proc. Natl. Acad. Sci. USA 117 29561 |
| [21] | Xiao L, Deng T S, Wang K, Zhu G, Wang Z, Yi W and Xue P 2020 Nat. Phys. 16 761 |
| [22] | Weidemann S, Kremer M, Helbig T, Hofmann T, Stegmaier A, Greiter M, Thomale R and Szameit A 2020 Science 368 311 |
| [23] | Kitagawa T, Rudner M S, Berg E and Demler E 2010 Phys. Rev. A 82 033429 |
| [24] | Kitagawa T, Berg E, Rudner M and Demler E 2010 Phys. Rev. B 82 235114 |
| [25] | Cayssol J, Dora B, Simon F and Moessner R 2013 Phys. Status Solidi RRL 7 101 |
| [26] | Barkhofen S, Nitsche T, Elster F, Lorz L, Gábris A, Jex I and Silberhorn C 2017 Phys. Rev. A 96 033846 |
| [27] | Asbóth J K and Obuse H 2013 Phys. Rev. B 88 121406(R) |
| [28] | Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Aspuru-Guzik A and White A G 2010 Phys. Rev. Lett. 104 153602 |
| [29] | Kitagawa T, Broome M A, Fedrizzi A, Rudner M S, Berg E, Kassal I, Aspuru-Guzik A, Demler E and White A G 2012 Nat. Commun. 3 882 |
| [30] | Zeuner J M, Rechtsman M C, Plotnik Y, Lumer Y, Nolte S, Rudner M S, Segev M and Szameit A 2015 Phys. Rev. Lett. 115 040402 |
| [31] | Zhan X, Xiao L, Bian Z, Wang K, Qiu X, Sanders B C, Yi W and Xue P 2017 Phys. Rev. Lett. 119 130501 |
| [32] | Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C and Xue P 2017 Nat. Phys. 13 1117 |
| [33] | Chen C, Ding X, Qin J, He Y, Luo Y H, Chen M C, Liu C, Wang X L, Zhang W J, Li H, You L X, Wang Z, Wang D W, Sanders B C, Lu C Y and Pan J W 2018 Phys. Rev. Lett. 121 100502 |
| [34] | Cardano F, Maffei M, Massa F, Piccirillo B, de Lisio C, De Filippis G, Cataudella V, Santamato E and Marrucci L 2016 Nat. Commun. 7 11439 |
| [35] | Cardano F, Errico A D, Dauphin A, Maffei M, Piccirillo B, de Lisio C, De Filippis G, Santamato V C E, Marrucci L, Lewenstein M and Massignan P 2017 Nat. Commun. 8 15516 |
| [36] | Rudner M S, Lindner N H, Berg E and Levin M 2013 Phys. Rev. X 3 031005 |
| [37] | Zhou L W and Gong J B 2018 Phys. Rev. B 98 205417 |
| [38] | Zhou L W and Pan J X 2019 Phys. Rev. A 100 053608 |
| [39] | Xie D, Deng T S, Xiao T, Gou W, Chen T, Yi W and Yan B 2020 Phys. Rev. Lett. 124 050502 |
| [40] | Schreiber A, Gábris A, Rohde P P, Laiho K, Štefaňák M, Potoček V, Hamilton C, Jex I and Silberhorn C 2012 Science 336 55 |
| [41] | Kawabata K, Shiozaki K, Ueda M and Sato M 2019 Phys. Rev. X 9 041015 |
| [42] | Yao S, Yan Z and Wang Z 2017 Phys. Rev. B 96 195303 |
| [43] | Bianco R and Resta R 2011 Phys. Rev. B 84 241106(R) |
| [44] | Caio M D, Möller G, Cooper N R and Bhaseen M J 2019 Nat. Phys. 15 257 |
| [45] | Privitera L and Santoro G E 2016 Phys. Rev. B 93 241406(R) |
| [46] | Pozo O, Repellin C and Grushin A G 2019 Phys. Rev. Lett. 123 247401 |
| [47] | Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801 |
| [48] | Wang K, Qiu X, Xiao L, Zhan X, Bian Z, Sanders B C, Yi W and Xue P 2019 Nat. Commun. 10 2293 |
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