Phase-Modulated 2D Topological Physics in a One-Dimensional Ultracold System
Gang-Feng Guo1 , Xi-Xi Bao1 , Lei Tan1* , and Huai-Qiang Gu2
1 Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China2 School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China
Abstract :We propose a one-dimensional optical lattice model to simulate and explore two-dimensional topological phases with ultracold atoms, considering the phases of the hopping strengths as an extra dimension. It is shown that the model exhibits nontrivial phases, and corresponding two chiral-edge states. Moreover, we demonstrate the connections between changes in the topological invariants and the Dirac points. Furthermore, the topological order detected by the particle pumping approach in cold atoms is also investigated. The results obtained here provide a feasible and flexible method of simulating and exploring high-dimensional topological phases in low-dimension systems via the controllable phase of the hopping strength.
收稿日期: 2020-12-14
出版日期: 2021-04-06
:
03.65.Vf
(Phases: geometric; dynamic or topological)
73.43.Nq
(Quantum phase transitions)
[1] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[2] Bansi A L, Lin H and Das T 2016 Rev. Mod. Phys. 88 021004
[3] Sheng L, Shao L B, Hou Q Z and Xue Z Y 2018 J. Phys.: Condens. Matter 30 124001
[4] Li L H, Xu Z H and Chen S 2014 Phys. Rev. B 89 085111
[5] Read N and Green D 2000 Phys. Rev. B 61 10267
[6] Kitaev A Y 2001 Phys. -Usp. 44 131
[7] Alicea J 2012 Rep. Prog. Phys. 75 076501
[8] Ruostekoski J, Dunne G V and Javanainen J 2002 Phys. Rev. Lett. 88 180401
[9] Thouless D J 1983 Phys. Rev. B 27 6083
[10] Rice M J and Mele E J 1982 Phys. Rev. Lett. 49 1455
[11] Yao S Y and Wang Z 2018 Phys. Rev. Lett. 121 086803
[12] Zhu S L, Wang B and Duan L M 2007 Phys. Rev. Lett. 98 260402
[13] Zhang D W, Wang Z D and Zhu S L 2012 Front. Phys. 7 31
[14] Tarruell L, Greif D, Uehlinger T, Jotzu G and Esslinger T 2012 Nature 483 302
[15] Lewenstein M, Sanpera A, Ahufnger V, Damski B, Sen(De) A and Sen U 2007 Adv. Phys. 56 243
[16] Jiang J H 2012 Phys. Rev. A 85 033640
[17] He W Y, Zhang S and Law K T 2016 Phys. Rev. A 94 013606
[18] Zhu S L, Fu H, Wu C J, Zhang S C and Duan L M 2006 Phys. Rev. Lett. 97 240401
[19] Wang P, Yu Z Q, Fu Z, Miao J, Huang L, Chai S, Zhai H and Zhang J 2012 Phys. Rev. Lett. 109 095301
[20] Cheuk L W, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S and Zwierlein M W 2012 Phys. Rev. Lett. 109 095302
[21] Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J and Pan J W 2016 Science 354 83
[22] Shao L B, Zhu S L, Sheng L, Xing D Y and Wang Z D 2008 Phys. Rev. Lett. 101 246810
[23] Deng D L, Wang S T and Duan L M 2014 Phys. Rev. A 90 041601
[24] Price H M and Cooper N R 2012 Phys. Rev. A 85 033620
[25] Alba E, Fernandez-Gonzalvo X, Mur-Petit J, Pachos J K and Garcia-Ripoll J J 2011 Phys. Rev. Lett. 107 235301
[26] Liu X J, Liu Z X and Cheng M 2013 Phys. Rev. Lett. 110 076401
[27] Zhu S L, Shao L B, Wang Z D and Duan L M 2011 Phys. Rev. Lett. 106 100404
[28] Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T, Nascimbene S, Cooper N R, Bloch I and Goldman N 2015 Nat. Phys. 11 162
[29] Abanin D A, Kitagawa T, Bloch I and Demler E 2013 Phys. Rev. Lett. 110 165304
[30] Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E and Bloch I 2013 Nat. Phys. 9 795
[31] Zhu Y Q, Zhang D W, Yan H, Xing D Y and Zhu S L 2017 Phys. Rev. A 96 033634
[32] Zhang D W, Zhao Y X, Liu R B, Xue Z Y, Zhu S L and Wang Z D 2016 Phys. Rev. A 93 043617
[33] Lang L J, Cai X and Chen S 2012 Phys. Rev. Lett. 108 220401
[34] Zhu S L, Wang Z D, Chan Y H and Duan L M 2013 Phys. Rev. Lett. 110 075303
[35] Wang L, Soluyanov A A and Troyer M 2013 Phys. Rev. Lett. 110 166802
[36] Ozawa T, Price H M, Goldman N, Zilberberg O and Carusotto I 2016 Phys. Rev. A 93 043827
[37] Price H M, Zilberberg O, Ozawa T, Carusotto I and Goldman N 2015 Phys. Rev. Lett. 115 195303
[38] Saito T Y and Furukawa S 2017 Phys. Rev. A 95 043613
[39] Ghosh S K, Greschner S, Yadav U K, Mishra T, Rizzi M and Shenoy V B 2017 Phys. Rev. A 95 063612
[40] Mei F, Zhu S L, Zhang Z M, Oh C H and Goldman N 2012 Phys. Rev. A 85 013638
[41] Liu X J, Law K T, Ng T K and Lee P A 2013 Phys. Rev. Lett. 111 120402
[42] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 Nature 515 237
[43] Yang D C, Cheng M T, Ma X S, Xu J P, Zhu C J and Huang X H 2018 Phys. Rev. A 98 063809
[44] Pleinert M O, von Zanthier J and Agarwal G S 2018 Phys. Rev. A 97 023831
[45] Wang C, Liu Y L, Wu R and Liu Y X 2017 Phys. Rev. A 96 013818
[46] Yuan L, Xu S and Fan S 2015 Opt. Lett. 40 5140
[47] Tena D, Colin J K, Ling L, Wolfgang K M S and Hrvoje B 2015 Phys. Rev. Lett. 114 225301
[48] Luo X W, Zhou X X, Xu J S, Li C F, Guo G C, Zhang C W and Zhou Z W 2017 Nat. Commun. 8 16097
[49] Fukui T, Hatsugai Y and Suzuki H 2005 J. Phys. Soc. Jpn. 74 1674
[50] Lu H I, Schemmer M, Aycock L M, Genkina D, Sugawa S and Spielman I B 2016 Phys. Rev. Lett. 116 200402
[51] Mei F, You J B, Zhang D W, Yang X C, Fazio R, Zhu S L and Kwek L C 2014 Phys. Rev. A 90 063638
[52] Zhang D W, Mei F, Xue Z Y, Zhu S L and Wang Z D 2015 Phys. Rev. A 92 013612
[1]
. [J]. 中国物理快报, 2023, 40(7): 70305-.
[2]
. [J]. 中国物理快报, 2022, 39(10): 100202-100202.
[3]
. [J]. 中国物理快报, 2022, 39(10): 104101-.
[4]
. [J]. 中国物理快报, 2022, 39(4): 47501-.
[5]
. [J]. 中国物理快报, 2022, 39(3): 30301-.
[6]
. [J]. 中国物理快报, 2022, 39(1): 17401-017401.
[7]
. [J]. 中国物理快报, 2022, 39(1): 10301-010301.
[8]
. [J]. 中国物理快报, 2021, 38(12): 127101-.
[9]
. [J]. 中国物理快报, 2021, 38(11): 110302-.
[10]
. [J]. 中国物理快报, 2021, 38(7): 70302-.
[11]
. [J]. 中国物理快报, 2021, 38(7): 77101-.
[12]
. [J]. 中国物理快报, 2021, 38(6): 60302-.
[13]
. [J]. 中国物理快报, 2021, 38(3): 30301-.
[14]
. [J]. 中国物理快报, 2020, 37(9): 97301-.
[15]
. [J]. 中国物理快报, 2020, 37(9): 90301-.