| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
|
|
|
|
Localization Dynamics at the Exceptional Point of Non-Hermitian Creutz Ladder |
| S. M. Zhang†, T. Y. He†, and L. Jin* |
| School of Physics, Nankai University, Tianjin 300071, China |
|
| Cite this article: |
|
S. M. Zhang, T. Y. He, and L. Jin 2024 Chin. Phys. Lett. 41 027201 |
|
|
|
|
Abstract We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry. Destructive interference generates a flat spectrum at the exceptional point, where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette. All excitations are completely confined within the localization area, unaffected by gain and loss. Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence, while multiple-site excitations may display oscillating or constant intensities at the exceptional point. These results provide insights into the fascinating dynamics of non-Hermitian localization, where level coalescence and degeneracy coexist at the exceptional point.
|
|
|
Received: 17 November 2023
Published: 07 February 2024
|
|
| PACS: |
72.15.Rn
|
(Localization effects (Anderson or weak localization))
|
| |
03.65.Vf
|
(Phases: geometric; dynamic or topological)
|
| |
42.25.Hz
|
(Interference)
|
|
|
|
|
|
| [1] | Feng L, El-Ganainy R, and Ge L 2017 Nat. Photonics 11 752 |
| [2] | Christodoulides D and Yang J 2018 Parity-Time Symmetry and Its Applications (Berlin: Springer) |
| [3] | El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, and Christodoulides D N 2018 Nat. Phys. 14 11 |
| [4] | Miri M A and Alù A 2019 Science 363 eaar7709 |
| [5] | Özdemir Ş K, Rotter S, Nori F, and Yang L 2019 Nat. Mater. 18 783 |
| [6] | Jin L and Song Z 2009 Phys. Rev. A 80 052107 |
| [7] | Jin L and Song Z 2010 Phys. Rev. A 81 032109 |
| [8] | Luo X B, Huang J H, Zhong H H, Qin X Z, Xie Q T, Kivshar Y S, and Lee C 2013 Phys. Rev. Lett. 110 243902 |
| [9] | Jin L and Song Z 2016 Phys. Rev. A 93 062110 |
| [10] | Zhang K L, Jin L, and Song Z 2019 Phys. Rev. B 100 144301 |
| [11] | Duan L W, Wang Y Z, and Chen Q H 2020 Chin. Phys. Lett. 37 081101 |
| [12] | Fu T, Wang Y F, Wang X Y, Zhou X Y, and Zheng W H 2020 Chin. Phys. Lett. 37 044207 |
| [13] | Xu H S and Jin L 2023 Phys. Rev. Res. 5 L042005 |
| [14] | Jin L 2018 Phys. Rev. A 97 012121 |
| [15] | Zhang S M, Zhang X Z, Jin L, and Song Z 2020 Phys. Rev. A 101 033820 |
| [16] | Jin L, Wu H C, Wei B B, and Song Z 2020 Phys. Rev. B 101 045130 |
| [17] | Wiersig J 2014 Phys. Rev. Lett. 112 203901 |
| [18] | Liu Z P, Zhang J, Özdemir Ş K, Peng B, Jing H, Lü X Y, Li C W, Yang L, Nori F, and Liu Y X 2016 Phys. Rev. Lett. 117 110802 |
| [19] | Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N, and Khajavikhan M 2017 Nature 548 187 |
| [20] | Chen W J, Özdemir Ş K, Zhao G M, Wiersig J, and Yang L 2017 Nature 548 192 |
| [21] | Chen C, Jin L, and Liu R B 2019 New J. Phys. 21 083002 |
| [22] | Lai Y H, Lu Y K, Suh M G, Yuan Z, and Vahala K 2019 Nature 576 65 |
| [23] | Hokmabadi M P, Schumer A, Christodoulides D N, and Khajavikhan M 2019 Nature 576 70 |
| [24] | Xu H, Mason D, Jiang L, and Harris J G E 2016 Nature 537 80 |
| [25] | Jin L and Song Z 2012 Phys. Rev. A 85 012111 |
| [26] | Ramezani H, Li H K, Wang Y, and Zhang X 2014 Phys. Rev. Lett. 113 263905 |
| [27] | Jin L, Zhang X Z, Zhang G, and Song Z 2016 Sci. Rep. 6 20976 |
| [28] | Gear J, Sun Y, Xiao S, Zhang L, Fitzgerald R, Rotter S, Chen H, and Li J 2017 New J. Phys. 19 123041 |
| [29] | Jin L and Song Z 2018 Phys. Rev. Lett. 121 073901 |
| [30] | Luo J, Li J, and Lai Y 2018 Phys. Rev. X 8 031035 |
| [31] | Jin L and Song Z 2021 Chin. Phys. Lett. 38 024202 |
| [32] | Jin L 2022 Chin. Phys. Lett. 39 037302 |
| [33] | Zhang K, Fang C, and Yang Z S 2023 Phys. Rev. Lett. 131 036402 |
| [34] | Liu C, Lan J, Gu Z M, and Zhu J 2023 Chin. Phys. Lett. 40 124301 |
| [35] | Ashida Y, Gong Z, and Ueda M 2020 Adv. Phys. 69 249 |
| [36] | Bergholtz E J, Budich J C, and Kunst F K 2021 Rev. Mod. Phys. 93 015005 |
| [37] | Ding K, Fang C, and Ma G 2022 Nat. Rev. Phys. 4 745 |
| [38] | Lin R J, Tai T, Li L H, and Lee C H 2023 Front. Phys. 18 53605 |
| [39] | Yao S Y and Wang Z 2018 Phys. Rev. Lett. 121 086803 |
| [40] | Yao S Y, Song F, and Wang Z 2018 Phys. Rev. Lett. 121 136802 |
| [41] | Song F, Yao S Y, and Wang Z 2019 Phys. Rev. Lett. 123 246801 |
| [42] | Zhang K, Yang Z S, and Fang C 2020 Phys. Rev. Lett. 125 126402 |
| [43] | Yang Z S, Zhang K, Fang C, and Hu J P 2020 Phys. Rev. Lett. 125 226402 |
| [44] | Zhang K, Yang Z, and Fang C 2022 Nat. Commun. 13 2496 |
| [45] | Jin L 2017 Phys. Rev. A 96 032103 |
| [46] | Jin L, Wang P, and Song Z 2017 Sci. Rep. 7 5903 |
| [47] | Jin L and Song Z 2019 Phys. Rev. B 99 081103(R) |
| [48] | Wu H C, Jin L, and Song Z 2019 Phys. Rev. B 100 155117 |
| [49] | Lin S, Jin L, and Song Z 2019 Phys. Rev. B 99 165148 |
| [50] | Zhang K L, Wu H C, Jin L, and Song Z 2019 Phys. Rev. B 100 045141 |
| [51] | Xiao L, Deng T S, Wang K K, Zhu G Y, Wang Z, Yi W, and Xue P 2020 Nat. Phys. 16 761 |
| [52] | Wang X R, Guo C X, Du Q, and Kou S P 2020 Chin. Phys. Lett. 37 117303 |
| [53] | Wu H C, Yang X M, Jin L, and Song Z 2020 Phys. Rev. B 102 161101(R) |
| [54] | Wu H C, Jin L, and Song Z 2021 Phys. Rev. B 103 235110 |
| [55] | Xie L C, Wu H C, Zhang X Z, Jin L, and Song Z 2021 Phys. Rev. B 104 125406 |
| [56] | Li T Y, Zhang Y S, and Yi W 2021 Chin. Phys. Lett. 38 030301 |
| [57] | Cao P C, Peng Y G, Li Y, and Zhu X F 2022 Chin. Phys. Lett. 39 057801 |
| [58] | Wang J H, Tao Y L, and Xu Y 2022 Chin. Phys. Lett. 39 010301 |
| [59] | Wang L W, Lin Z K, and Jiang J H 2023 Phys. Rev. B 108 195126 |
| [60] | Liu Z F and Huang J P 2023 Chin. Phys. Lett. 40 110305 |
| [61] | Masumoto N, Kim N Y, Byrnes T, Kusudo K, Löffler A, Höfling S, Forchel A, and Yamamoto Y 2012 New J. Phys. 14 065002 |
| [62] | Flach S, Leykam D, Bodyfelt J D, Matthies P, and Desyatnikov A S 2014 Europhys. Lett. 105 30001 |
| [63] | Bodyfelt J D, Leykam D, Danieli C, Yu X, and Flach S 2014 Phys. Rev. Lett. 113 236403 |
| [64] | Jacqmin T, Carusotto I, Sagnes I, Abbarchi M, Solnyshkov D D, Malpuech G, Galopin E, Lemaître A, Bloch J, and Amo A 2014 Phys. Rev. Lett. 112 116402 |
| [65] | Morales-Inostroza L and Vicencio R A 2016 Phys. Rev. A 94 043831 |
| [66] | Leykam D, Andreanov A, and Flach S 2018 Adv. Phys.: X 3 1473052 |
| [67] | Zhang S M and Jin L 2020 Phys. Rev. B 102 054301 |
| [68] | Guzmán-Silva D, Mejía-Cortés C, Bandres M A, Rechtsman M C, Weimann S, Nolte S, Segev M, Szameit A, and Vicencio R A 2014 New J. Phys. 16 063061 |
| [69] | Mukherjee S and Thomson R R 2015 Opt. Lett. 40 5443 |
| [70] | Vicencio R A, Cantillano C, Morales-Inostroza L, Real B, Mejía-Cortés C, Weimann S, Szameit A, and Molina M I 2015 Phys. Rev. Lett. 114 245503 |
| [71] | Mukherjee S, Spracklen A, Choudhury D, Goldman N, Öhberg P, Andersson E, and Thomson R R 2015 Phys. Rev. Lett. 114 245504 |
| [72] | Molina M I 2015 Phys. Rev. A 92 063813 |
| [73] | Ge L 2015 Phys. Rev. A 92 052103 |
| [74] | Ramezani H 2017 Phys. Rev. A 96 011802(R) |
| [75] | Biesenthal T, Kremer M, Heinrich M, and Szameit A 2019 Phys. Rev. Lett. 123 183601 |
| [76] | Qi B K, Zhang L X, and Ge L 2018 Phys. Rev. Lett. 120 093901 |
| [77] | Jin L 2019 Phys. Rev. A 99 033810 |
| [78] | Zhang S M and Jin L 2019 Phys. Rev. A 100 043808 |
| [79] | Zhang S M, Xu H S, and Jin L 2023 Phys. Rev. A 108 023518 |
| [80] | Zhang X Z, Jin L, and Song Z 2012 Phys. Rev. A 85 012106 |
| [81] | Vidal J, Mosseri R, and Douçot B 1998 Phys. Rev. Lett. 81 5888 |
| [82] | Mukherjee S, Di Liberto M, Öhberg P, Thomson R R, and Goldman N 2018 Phys. Rev. Lett. 121 075502 |
| [83] | Kremer M, Petrides I, Meyer E, Heinrich M, Zilberberg O, and Szameit A 2020 Nat. Commun. 11 907 |
| [84] | Longhi S 2014 Opt. Lett. 39 5892 |
| [85] | Gligorić G, Beličev P P, Leykam D, and Maluckov A 2019 Phys. Rev. A 99 013826 |
| [86] | Di Liberto M, Mukherjee S, and Goldman N 2019 Phys. Rev. A 100 043829 |
| [87] | Danieli C, Andreanov A, Mithun T, and Flach S 2021 Phys. Rev. B 104 085131 |
| [88] | Cai H, Liu J, Wu J, He Y, Zhu S Y, Zhang J X, and Wang D W 2019 Phys. Rev. Lett. 122 023601 |
| [89] | Kang J H, Han J H, and Shin Y 2020 New J. Phys. 22 013023 |
| [90] | Kuno Y 2020 Phys. Rev. B 101 184112 |
| [91] | Wang P, Jin L, and Song Z 2019 Phys. Rev. A 99 062112 |
| [92] | Sun N and Lim L K 2017 Phys. Rev. B 96 035139 |
| [93] | Alaeian H, Chang C W S, Moghaddam M V, Wilson C M, Solano E, and Rico E 2019 Phys. Rev. A 99 053834 |
| [94] | Hung J S C, Busnaina J H, Chang C W S, Vadiraj A M, Nsanzineza I, Solano E, Alaeian H, Rico E, and Wilson C M 2021 Phys. Rev. Lett. 127 100503 |
| [95] | Xu H S and Jin L 2022 Phys. Rev. Res. 4 L032015 |
| [96] | Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O, and Carusotto I 2019 Rev. Mod. Phys. 91 015006 |
| [97] | Goldman N and Dalibard J 2014 Phys. Rev. X 4 031027 |
| [98] | Hafezi M 2014 Int. J. Mod. Phys. B 28 1441002 |
| [99] | Xie L C, Jin L, and Song Z 2023 Sci. Bull. 68 255 |
| [100] | Sounas D L and Alù A 2017 Nat. Photonics 11 774 |
| [101] | Miri M A, Ruesink F, Verhagen E, and Alù A 2017 Phys. Rev. Appl. 7 064014 |
| [102] | Fan L, Wang J, Varghese L T, Shen H, Niu B, Xuan Y, Weiner A M, and Qi M 2012 Science 335 447 |
| [103] | Jin L and Song Z 2011 Phys. Rev. A 84 042116 |
| [104] | Zhang S M and Jin L 2020 Phys. Rev. Res. 2 033127 |
| [105] | Gligorić G, Leykam D, and Maluckov A 2020 Phys. Rev. A 101 023839 |
| [106] | Longhi S 2021 Opt. Lett. 46 2872 |
| [107] | Li H, Dong Z L, Longhi S, Liang Q, Xie D Z, and Yan B 2022 Phys. Rev. Lett. 129 220403 |
| [108] | Zhan X, Xiao L, Bian Z, Wang K, Qiu X, Sanders B C, Yi W, and Xue P 2017 Phys. Rev. Lett. 119 130501 |
| [109] | Wang K K, Qiu X Z, Xiao L, Zhan Z, Bian Z H, Sanders B C, Yi W, and Xue P 2019 Nat. Commun. 10 2293 |
| [110] | Wang P, Jin L, Zhang G, and Song Z 2016 Phys. Rev. A 94 053834 |
| [111] | Li C, Jin L, and Song Z 2017 Phys. Rev. A 95 022125 |
| [112] | Zhong Q, Christodoulides D N, Khajavikhan M, Makris K G, and El-Ganainy R 2018 Phys. Rev. A 97 020105(R) |
| [113] | Xu H S, Xie L C, and Jin L 2023 Phys. Rev. A 107 062209 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
