1 Aharonov Y, Davidovich L and Zagury N 1993 Phys. Rev. A 48 1687 2 Kempe J 2003 Comtemporary Physics 44 307 3 Wang J B and Manouchehri K 2013 Physical implementation of quantum walks(Berlin: Springer) 4 Bouwmeester D, Marzoli I, Karman G P, Schleich W and Woerdman J P 1999 Phys. Rev. A 61 013410 5 Karski M, F\"orster L, Choi J M, Steffen A, Alt W, Meschede D and Widera A 2009 Science 325 174 6 Preiss P M, Ma R, Tai M E, Lukin A, Rispoli M, Zupancic P, Islam R and Greiner M 2015 Science 347 1229 7 Ramasesh V V, Flurin E, Rudner M, Siddiqi I and Yao N Y 2017 Phys. Rev. Lett. 118 130501 8 Yan Z G, Zhang Y R, Gong M, Wu Y L, Zheng Y R, Li S W, Wang C, Liang F T, Lin J, Xu Y, Guo C, Sun L, Peng C Z, Xia K Y, Deng H, Rong H, You J Q, Nori F, Fan H, Zhu X B and Pan J W 2019 Science 364 753 9 Ye Y S, Ge Z Y, Wu Y L, Wang S Y, Gong M, Zhang Y R, Zhu Q L, Yang R, Li S W, Liang F T, Lin J, Xu Y, Guo C, Sun L H, Cheng C, Ma N S, Meng Z Y, Deng H, Rong H, Lu C Y, Peng C Z, Fan H, Zhu X B and Pan J W 2019 Phys. Rev. Lett. 123 050502 10 Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Aspuru-Guzik A and White A G 2010 Phys. Rev. Lett. 104 153602 11 Xue P, Zhang R, Qin H, Zhan X, Bian Z H, Li J and Sanders B C 2015 Phys. Rev. Lett. 114 140502 12 Schmitz H, Matjeschk R, Schneider C, Glueckert J, Enderlein M, Huber T and Schaetz T 2009 Phys. Rev. Lett. 103 090504 13 Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R and Osellame R 2012 Phys. Rev. Lett. 108 010502 14 Du J F, Li H, Xu X D, Shi M J, Wu J H, Zhou X Y and Han R D 2003 Phys. Rev. A 67 042316 15 Kitagawa T, Rudner M S, Berg E and Demler E 2010 Phys. Rev. A 82 033429 16 Kitagawa T, Broome M A, Fedrizzi A, Rudner M S, Berg E, Kassal I, Aspuru Guizik A, Demler E and White A G 2012 Nat. Commun. 3 882 17 Flurin E, Ramasesh V V, Hacohen-Gourgy S, Martin L S, Yao N Y and Siddiqi I 2017 Phys. Rev. X 7 031023 18 Benedetti C, Buscemi F and Bordone P 2012 Phys. Rev. A 85 042314 19 Qin X Z, Ke Y G, Guan X W, Li Z B, Andrei N and Lee C H 2014 Phys. Rev. A 90 062301 20 Wang L, Hao Y and Chen S 2008 Eur. Phys. J. D 48 229 21 Lahini Y, Verbin M, Huber S D, Bromberg Y, Pugatch R and Silberberg Y 2012 Phys. Rev. A 86 011603 22 Wang L, Hao Y J and Chen S 2010 Phys. Rev. A 81 063637 23 Wang L M, Wang L and Zhang Y B 2014 Phys. Rev. A 90 063618 24 Gan S, He X D, Liu B, Feng C D 2015 Chin. Phys. Lett. 32 080305 25 Yin Y, Katsanos D E and Evangelou S N 2008 Phys. Rev. A 77 022302 26 Beggi A, Buscemi F and Bordone P 2016 Quantum Inf. Proc. 15 3711 27 Zhao J, Hu Y Y, Tong P Q 2015 Chin. Phys. Lett. 32 060501 28 Li Z J, Izaac J A and Wang J B 2013 Phys. Rev. A 87 012314 29 Li Z J, Wang J B 2015 Sci. Rep. 5 13585 30 Kraus Y E, Lahini Y, Ringel Z, Verbin M and Zilberberg O 2012 Phys. Rev. Lett. 109 106402 31 Wang L, Liu N, Chen S and Zhang Y B 2015 Phys. Rev. A 92 053606 32 Wang L, Liu N, Chen S and Zhang Y B 2017 Phys. Rev. A 95 013619 33 Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 34 Bender C M, Brody D C and Jones H F 2002 Phys. Rev. Lett. 89 270401 35 Bender C M 2007 Rep. Prog. Phys. 70 947 36 Moiseyev N 2011 Non-Hermitian Quantum Mechanics (England: Cambridge University Press) 37 Shen H T, Zhen B and Fu L 2018 Phys. Rev. Lett. 120 146402 39 Yin C H, Jiang H, Li L H, L\"u R and Chen S 2018 Phys. Rev. A 97 052115 40 Shen H T and Fu L 2018 Phys. Rev. Lett. 121 026403 41 Budich J C, Carlstr\"om J, Kunst F K and Bergholtz E J 2019 Phys. Rev. B 99 041406 42 Yang Z S and Hu J P 2019 Phys. Rev. B 99 081102 43 Liu C H, Jiang H and Chen S 2019 Phys. Rev. B 99 125103 44 Chen Y and Zhai H 2018 Phys. Rev. B 98 245130 45 Yoshida T, Peters R, Kawakami N and Hatsugai Y 2019 Phys. Rev. B 99 121101 46 Wu Y, Liu W Q, Geng J P, Song X R, Ye X Y, Duan C K, Rong X and Du J F 2019 Science 364 878 47 Zeng Q B, Zhu B G, Chen S, You L and L\"u R 2016 Phys. Rev. A 94 022119 48 Li C, Zhang X Z, Zhang G and Song Z 2018 Phys. Rev. B 97 115436 49 Kawabata K, Ashida Y, Katsura H and Ueda M 2018 Phys. Rev. B 98 085116 50 Xu Y, Wang S T and Duan L M 2017 Phys. Rev. Lett. 118 045701 51 Gong Z P, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079 52 Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N and Peschel U 2012 Nature 488 167 53 Wang X R, Guo C X and Kou S P 2020 Phys. Rev. B 101 121116 54 Harari G, Bandres M A, Lumer Y, Rechtsman M C, Chong Y D, Khajavikhan M, Christodoulides D N and Segev M 2018 Science 359 eaar4003 55 Bandres M A, Wittek S, Harari G, Parto M, Ren J, Segev M, Chritodoulides D N and Khajavikhan M 2018 Science 359 eaar4005 56 Bahari B, Ndao A, Vallini F, Amili A E, Fainman Y and Kant\'e B 2017 Science 358 636 57 Mochizuki K, Kim D and Obuse H 2016 Phys. Rev. A 93 062116 58 Song F, Yao S Y and Wang Z 2019 Phys. Rev. Lett. 123 170401 59 Pan L, Wang X L, Cui X L and Chen S 2020 Phys. Rev. A 102 023306 60 Diehl S, Rico E, Baranov M A and Zoller P 2011 Nat. Phys. 7 971 61 Verstraete F, Wolf M M and Ignacio Cirac J I 2009 Nat. Phys. 5 633 62 Rudner M S and Levitov L S 2009 Phys. Rev. Lett. 102 065703 63 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 64 Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E and Bloch I 2013 Nat. Phys. 9 795 65 Tomita T, Nakajima S, Danshita I, Takasu Y and Takahashi Y 2017 Sci. Adv. 3 e1701513 66 Tomita T, Nakajima S, Takasu Y and Takahashi Y 2019 Phys. Rev. A 99 031601(R) 67 Jacqmin T, Carusotto I, Sagnes I, Abbarchi M, Solnyshkov D D, Malpuech G, Galopin E, Lema\itre A,, Bloch J and Amo A 2014 Phys. Rev. Lett. 112 116402 69 Gao T, Estrecho E, Bliokh K Y, Liew T C H, Fraser M D, Brodbeck S, Kamp M, Schneider C, H\"ofling S, Yamamoto Y, Nori F and Kivshar Y S 2015 Nature 526 554 70 Martinez Alvarez V M, Barrios Vargas J E, Berdakin M and Foa Torres L E 2018 Eur. Phys. J. Spec. Top. 227 1295 71 Leykam D, Bliokh K Y, Huang C, Chong Y D and Nori F 2017 Phys. Rev. Lett. 118 040401 72 Xiong Y 2018 J. Phys. Commun. 2 035043 73 Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401 74 Jin L and Song Z 2019 Phys. Rev. B 99 081103 75 Herviou L, Bardarson J H and Regnault N 2019 Phys. Rev. A 99 052118 77 Deng T S and Yi W 2019 Phys. Rev. B 100 035102 78 Lee T E 2016 Phys. Rev. Lett. 116 133903 79 Yao S Y and Wang Z 2018 Phys. Rev. Lett. 121 086803 80 Yokomizo K and Murakami S 2019 Phys. Rev. Lett. 123 066404 81 Borgnia D S, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802 82 Zhang K, Yang Z S and Fang C 2020 Phys. Rev. Lett. 125 126402 83 Yang Z H, Zhang K, Fang C and Hu J P 2020 arXiv: 1912.05499 [cond-mat.mes-hall]) 84 Yi Y F and Yang Z S 2020 Phys. Rev. Lett. 125 186802) 85 Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808 86 Song F, Yao S Y and Wang Z 2019 Phys. Rev. Lett. 123 246801 87 Zhan X, Xiao L, Bian Z H, Wang K K, Qiu X Z, Sanders B C, Yi W and Xue P 2017 Phys. Rev. Lett. 119 130501 88 Xiao L, Deng T S, Wang K K, Zhu G Y, Wang Z, Yi W and Xue P 2020 Nat. Phys. 16 761 89 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 90 Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005 91 Hafezi M, Demler E A, Lukin M D and Taylor J M 2011 Nat. Phys. 7 907 92 Viyuela O, Vodola D, Pupillo G and Martin-Delgado M A 2016 Phys. Rev. B 94 125121 |