搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

动力学淬火过程中的不动点及衍生拓扑现象

邓天舒 易为

引用本文:
Citation:

动力学淬火过程中的不动点及衍生拓扑现象

邓天舒, 易为

Fixed points and dynamic topological phenomena in quench dynamics

Deng Tian-Shu, Yi Wei
PDF
HTML
导出引用
  • 本文对近两年来有关淬火动力学过程中拓扑现象的研究做简要综述. 这些动力学拓扑现象被动力学过程中的衍生拓扑不变量保护, 与淬火前后体系的拓扑性质有密切关系. 基于人工量子模拟平台的高度可控性, 已在诸如超冷原子、超导量子比特、核磁共振、线性光学等众多物理体系中, 通过对人工拓扑体系动力学过程的调控, 观测到如动力学涡旋、动量-时间域的Hopf映射及环绕数、拓扑保护的自旋环结构、动力学量子相变、动量-时间斯格明子等诸多动力学拓扑现象. 其中某些拓扑结构还可以在非幺正动力学淬火过程中稳定存在. 这些研究将人们对拓扑物相的认识和研究从平衡态推广到非平衡动力学领域, 具有重要的科学价值.
    In this review, we discuss the recent progress on the study of dynamic topological phenomena in quench dynamics. In particular, we focus on dynamic quantum phase transition and dynamic topological invariant, both of which are hinged upon the existence of fixed points in the dynamics. Further, the existence of these fixed points are topologically protected, in the sense that their existence are closely related to static topological invariants of pre- and post-quench Hamiltonians. We also discuss under what condition these dynamic topological phenomena are robust in non-unitary quench dynamics governed by non-Hermitian Hamiltonians. So far, dynamic topological phenomena have been experimentally observed in synthetic systems such as cold atomic gases, superconducting qubits, and linear optics. These studies extend our understanding of topological matter to the non-equilibrium regime.
      通信作者: 易为, wyiz@ustc.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 15522545)资助的课题.
      Corresponding author: Yi Wei, wyiz@ustc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 15522545).
    [1]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045Google Scholar

    [2]

    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057Google Scholar

    [3]

    Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237Google Scholar

    [4]

    Fläschner N, Rem B S, Tarnowski M, Vogel D, Lühmann D S, Sengstock K, Weitenberg C 2016 Science 352 1091Google Scholar

    [5]

    Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J, Pan J W 2016 Science 354 83Google Scholar

    [6]

    Song B, Zhang L, He C, Poon T F J, Haiiyev E, Zhang S, Liu X J, Jo G B 2018 Sci. Adv. 4 4748Google Scholar

    [7]

    Poli C, Bellec M, Kuhl U, Mortessagne F, Schomerus H 2015 Nat. Commun. 6 6710Google Scholar

    [8]

    Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A 2017 Nat. Mater. 16 433Google Scholar

    [9]

    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, Xue P 2017 Nat. Phys. 13 1117Google Scholar

    [10]

    Zeuner J M, Rechtsman M C, Plotnik Y, Lumer Y, Nolte S, Rudner M S, Segev M, Szameit A 2015 Phys. Rev. Lett. 115 040402Google Scholar

    [11]

    Zhan X, Xiao L, Bian Z, Wang K, Qiu X, Sanders B C, Yi W, Xue P 2017 Phys. Rev. Lett. 119 130501Google Scholar

    [12]

    Shen H, Zhen B, Fu L 2018 Phys. Rev. Lett. 120 146402Google Scholar

    [13]

    Chen Y, Zhai H 2018 Phys. Rev. B 98 245130

    [14]

    Kunst F K, Edvardsson E, Budich J C, Bergholtz E J 2018 Phys. Rev. Lett. 121 026808Google Scholar

    [15]

    Yao S, Wang Z 2018 Phys. Rev. Lett. 121 086803Google Scholar

    [16]

    Yao S, Song F, Wang Z 2018 Phys. Rev. Lett. 121 136802Google Scholar

    [17]

    Caio M D, Cooper N R, Bhaseen M J 2015 Phys. Rev. Lett. 115 236403Google Scholar

    [18]

    D’Alessio L, Rigol M 2015 Nat. Commun. 6 8336Google Scholar

    [19]

    Wang C, Zhang P, Chen X, Yu J, Zhai H 2017 Phys. Rev. Lett. 118 185701Google Scholar

    [20]

    Yang C, Li L, Chen S 2018 Phys. Rev. B 97 060304Google Scholar

    [21]

    Gong Z, Ueda M 2018 Phys. Rev. Lett. 121 250601

    [22]

    Zhang L, Zhang L, Niu S, Liu X J 2018 Science Bulletin 63 1385Google Scholar

    [23]

    Zhang L, Zhang L, Liu X J 2018 arXiv: 1807.10782 [cond-mat.quant-gas]

    [24]

    Fläschner N, Vogel D, Tarnowski M, Rem B S, Lühmann D S, Heyl M, Budich J C, Mathey L, Sengstock K, Weitenberg C 2018 Nat. Phys. 14 265Google Scholar

    [25]

    Tarnowski M, Nur-Unal F, Flaschner N, Rem B S, Eckard A, Sengstock K, Weitenberg C 2017 arXiv:1709.01046 [cond-mat.quant-gas]

    [26]

    Sun W, Yi C R, Wang B Z, Zhang W W, Sanders B C, Xu X T, Wang Z Y, Schmiedmayer J, Deng Y J, Liu X J, Chen S, Pan J W 2018 Phys. Rev. Lett. 121 250403

    [27]

    Guo X Y, Yang C, Zeng Y, Peng Y, Li H K, Deng H, Jin Y R, Chen S, Zheng D N, Fan H 2018 arXiv:1806.09269 [cond-mat.stat-mech]

    [28]

    Wang K, Qiu X, Xiao L, Zhan X, Bina Z, Yi W, Xue P 2019 Phys. Rev. Lett. 122 020501

    [29]

    Tian T, Ke K, Zhang L, Lin L, Shi Z, Huang P, Lee C, Du J 2018 arXiv:1807.04483 [quant-ph]

    [30]

    Xu X Y, Wang Q Q, Heyl M, Budich J C, Pan W W, Chen Z, Jan M, Sun K, Xu J S, Han Y J, Li C F, Guo G C 2018 arXiv:1808.03930 [quant-ph]

    [31]

    Wang K, Qiu X, Xiao L, Zhan X, Bian Z, Yi W, Xue P 2018 arXiv:1808.06446 [quant-ph]

    [32]

    Heyl M, Polkovnikov A, Kehrein S 2013 Phys. Rev. Lett. 110 135704Google Scholar

    [33]

    Heyl M 2015 Phys. Rev. Lett. 115 140602Google Scholar

    [34]

    Heyl M 2018 Rep. Prog. Phys. 81 054001Google Scholar

    [35]

    Budich J C, Heyl M 2016 Phys. Rev. B 93 085416Google Scholar

    [36]

    Huang Z, Balatsky A V 2016 Phys. Rev. Lett. 117 086802Google Scholar

    [37]

    Vajna S, Dora B 2015 Phys. Rev. B 91 155127Google Scholar

    [38]

    Zhou L W, Wang Q H, Wang H L 2018 Phys. Rev. A 98 022129Google Scholar

    [39]

    Gu J, Sun K 2016 Phys. Rev. B 94 12511Google Scholar

    [40]

    Qiu X, Deng T S, Guo G C, Yi W 2018 Phys. Rev. A 98 021601Google Scholar

    [41]

    Qiu X, Deng T S, Hu Y, Xue P, Yi W 2018 arXiv:1806.10268[cond-mat.quant-gas]

    [42]

    Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar

    [43]

    Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401Google Scholar

    [44]

    Bender C M 2007 Rep. Prog. Phys. 70 947Google Scholar

    [45]

    Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698Google Scholar

    [46]

    Zhu B, Lu R, Chen S 2014 Phys. Rev. A 89 062102Google Scholar

    [47]

    Garrison J, Wright E 1988 Phys. Lett. A 128 177Google Scholar

    [48]

    Brody D C 2014 J. Phys. A: Math. Theor. 47 035305Google Scholar

    [49]

    Li J, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L 2016 arXiv:1608.05061[cond-mat.quant-gas]

    [50]

    Kohei K, Yuto A, Hosho K, Masahito U 2018 Phys. Rev. B 98 085116Google Scholar

  • 图 1  Bloch球上的动力学演化 (a) 态矢量在Bloch球上绕$ {h}^f $运动; (b) 动力学不动点对应于$ {h}^i\cdot {h}^f=\pm 1 $; (c) 临界点对应于$ {h} ^i\cdot {h}^f=0 $. 实线代表$ {h}^i $(绿色)与$ {h}^f $(红色), 虚线代表态矢量; 假设初态处于$ H_k $基态上, 即$ t=0 $时态矢量与$ {h}^i $方向相反

    Fig. 1.  Visualizing dynamics on the Bloch sphere: (a) State vector revolving around the $ {h}^f $ axis; (b) illustration of fixed points when $ {h}^i\cdot {h}^f=\pm 1 $; (c) illustration of critical points with $ {h} ^i\cdot {h}^f=0 $.

    图 2  淬火前后哈密顿量具有不同拓扑数时的典型斯格明子结构. 黑色箭头为自旋在平面内方向, 背景颜色对应自旋在与平面垂直方向上的分量大小, 蓝色对应向内, 黄色对应向外. 竖直虚线为不动点位置, 红色实线表示不同动量$ k $点的周期

    Fig. 2.  Momentum-time skyrmions when pre- and post-quench Hamiltonians possess different winding numbers.

    图 3  非厄米SSH模型及其拓扑相图 (a) 非厄米SSH模型. 在厄米SSH模型的基础上, 每个格点上均有增益或损耗; (b) 体系拓扑相图. 实线为拓扑边界, 虚线为宇称-时间对称与对称破缺区域的边界. $ v $, $ w $为SSH模型的跃迁系数, $ u $为增益损耗系数, $ \nu $为绕数

    Fig. 3.  Non-Hermitian SSH model and its topological phase diagram: (a) Non-Hermitian SSH model; (b) topological phase diagram.

    图 4  非厄密SSH模型淬火中的典型动力学自由能$ g(t) $与动力学拓扑序参量$ \nu^D(t) $ (a) 动力学自由能$ g(t) $; (b) 动力学拓扑序参量$ \nu^D(t) $. 在非厄米淬火过程中存在两个临界时间尺度及两个动力学拓扑序参量

    Fig. 4.  Dynamic free energy $ g(t) $ and dynamic topological order parameter $ \nu^D(t) $ in the quench dynamics of non-Hermitian SSH model: (a) Dynamic free energy $ g(t) $; (b) dynamic topological order parameter $ \nu^D(t) $.

  • [1]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045Google Scholar

    [2]

    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057Google Scholar

    [3]

    Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237Google Scholar

    [4]

    Fläschner N, Rem B S, Tarnowski M, Vogel D, Lühmann D S, Sengstock K, Weitenberg C 2016 Science 352 1091Google Scholar

    [5]

    Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J, Pan J W 2016 Science 354 83Google Scholar

    [6]

    Song B, Zhang L, He C, Poon T F J, Haiiyev E, Zhang S, Liu X J, Jo G B 2018 Sci. Adv. 4 4748Google Scholar

    [7]

    Poli C, Bellec M, Kuhl U, Mortessagne F, Schomerus H 2015 Nat. Commun. 6 6710Google Scholar

    [8]

    Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A 2017 Nat. Mater. 16 433Google Scholar

    [9]

    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, Xue P 2017 Nat. Phys. 13 1117Google Scholar

    [10]

    Zeuner J M, Rechtsman M C, Plotnik Y, Lumer Y, Nolte S, Rudner M S, Segev M, Szameit A 2015 Phys. Rev. Lett. 115 040402Google Scholar

    [11]

    Zhan X, Xiao L, Bian Z, Wang K, Qiu X, Sanders B C, Yi W, Xue P 2017 Phys. Rev. Lett. 119 130501Google Scholar

    [12]

    Shen H, Zhen B, Fu L 2018 Phys. Rev. Lett. 120 146402Google Scholar

    [13]

    Chen Y, Zhai H 2018 Phys. Rev. B 98 245130

    [14]

    Kunst F K, Edvardsson E, Budich J C, Bergholtz E J 2018 Phys. Rev. Lett. 121 026808Google Scholar

    [15]

    Yao S, Wang Z 2018 Phys. Rev. Lett. 121 086803Google Scholar

    [16]

    Yao S, Song F, Wang Z 2018 Phys. Rev. Lett. 121 136802Google Scholar

    [17]

    Caio M D, Cooper N R, Bhaseen M J 2015 Phys. Rev. Lett. 115 236403Google Scholar

    [18]

    D’Alessio L, Rigol M 2015 Nat. Commun. 6 8336Google Scholar

    [19]

    Wang C, Zhang P, Chen X, Yu J, Zhai H 2017 Phys. Rev. Lett. 118 185701Google Scholar

    [20]

    Yang C, Li L, Chen S 2018 Phys. Rev. B 97 060304Google Scholar

    [21]

    Gong Z, Ueda M 2018 Phys. Rev. Lett. 121 250601

    [22]

    Zhang L, Zhang L, Niu S, Liu X J 2018 Science Bulletin 63 1385Google Scholar

    [23]

    Zhang L, Zhang L, Liu X J 2018 arXiv: 1807.10782 [cond-mat.quant-gas]

    [24]

    Fläschner N, Vogel D, Tarnowski M, Rem B S, Lühmann D S, Heyl M, Budich J C, Mathey L, Sengstock K, Weitenberg C 2018 Nat. Phys. 14 265Google Scholar

    [25]

    Tarnowski M, Nur-Unal F, Flaschner N, Rem B S, Eckard A, Sengstock K, Weitenberg C 2017 arXiv:1709.01046 [cond-mat.quant-gas]

    [26]

    Sun W, Yi C R, Wang B Z, Zhang W W, Sanders B C, Xu X T, Wang Z Y, Schmiedmayer J, Deng Y J, Liu X J, Chen S, Pan J W 2018 Phys. Rev. Lett. 121 250403

    [27]

    Guo X Y, Yang C, Zeng Y, Peng Y, Li H K, Deng H, Jin Y R, Chen S, Zheng D N, Fan H 2018 arXiv:1806.09269 [cond-mat.stat-mech]

    [28]

    Wang K, Qiu X, Xiao L, Zhan X, Bina Z, Yi W, Xue P 2019 Phys. Rev. Lett. 122 020501

    [29]

    Tian T, Ke K, Zhang L, Lin L, Shi Z, Huang P, Lee C, Du J 2018 arXiv:1807.04483 [quant-ph]

    [30]

    Xu X Y, Wang Q Q, Heyl M, Budich J C, Pan W W, Chen Z, Jan M, Sun K, Xu J S, Han Y J, Li C F, Guo G C 2018 arXiv:1808.03930 [quant-ph]

    [31]

    Wang K, Qiu X, Xiao L, Zhan X, Bian Z, Yi W, Xue P 2018 arXiv:1808.06446 [quant-ph]

    [32]

    Heyl M, Polkovnikov A, Kehrein S 2013 Phys. Rev. Lett. 110 135704Google Scholar

    [33]

    Heyl M 2015 Phys. Rev. Lett. 115 140602Google Scholar

    [34]

    Heyl M 2018 Rep. Prog. Phys. 81 054001Google Scholar

    [35]

    Budich J C, Heyl M 2016 Phys. Rev. B 93 085416Google Scholar

    [36]

    Huang Z, Balatsky A V 2016 Phys. Rev. Lett. 117 086802Google Scholar

    [37]

    Vajna S, Dora B 2015 Phys. Rev. B 91 155127Google Scholar

    [38]

    Zhou L W, Wang Q H, Wang H L 2018 Phys. Rev. A 98 022129Google Scholar

    [39]

    Gu J, Sun K 2016 Phys. Rev. B 94 12511Google Scholar

    [40]

    Qiu X, Deng T S, Guo G C, Yi W 2018 Phys. Rev. A 98 021601Google Scholar

    [41]

    Qiu X, Deng T S, Hu Y, Xue P, Yi W 2018 arXiv:1806.10268[cond-mat.quant-gas]

    [42]

    Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar

    [43]

    Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401Google Scholar

    [44]

    Bender C M 2007 Rep. Prog. Phys. 70 947Google Scholar

    [45]

    Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698Google Scholar

    [46]

    Zhu B, Lu R, Chen S 2014 Phys. Rev. A 89 062102Google Scholar

    [47]

    Garrison J, Wright E 1988 Phys. Lett. A 128 177Google Scholar

    [48]

    Brody D C 2014 J. Phys. A: Math. Theor. 47 035305Google Scholar

    [49]

    Li J, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L 2016 arXiv:1608.05061[cond-mat.quant-gas]

    [50]

    Kohei K, Yuto A, Hosho K, Masahito U 2018 Phys. Rev. B 98 085116Google Scholar

  • [1] 曾超, 毛一屹, 吴骥宙, 苑涛, 戴汉宁, 陈宇翱. 一维超冷原子动量光晶格中的手征对称性破缺拓扑相. 物理学报, 2024, 73(4): 040301. doi: 10.7498/aps.73.20231566
    [2] 尹相国, 于海如, 郝亚江, 张云波. 一维接触排斥相互作用单自旋翻转费米气体的基态和淬火动力学性质. 物理学报, 2024, 73(2): 020302. doi: 10.7498/aps.73.20231425
    [3] 谭辉, 曹睿, 李永强. 基于动力学平均场的光晶格超冷原子量子模拟. 物理学报, 2023, 72(18): 183701. doi: 10.7498/aps.72.20230701
    [4] 苑涛, 戴汉宁, 陈宇翱. 超冷原子动量光晶格中的非线性拓扑泵浦. 物理学报, 2023, 72(16): 160302. doi: 10.7498/aps.72.20230740
    [5] 李庆鑫, 黄焱, 陈以威, 朱雨剑, 朱旺, 宋珺威, 安冬冬, 甘祺康, 王开元, 王浩林, 麦志洪, Andy Shen, 郗传英, 张警蕾, 于葛亮, 王雷. 双层石墨烯中的偶数分母分数量子霍尔态. 物理学报, 2022, 71(18): 187202. doi: 10.7498/aps.71.20220905
    [6] 孙孔浩, 易为. 非厄米局域拓扑指标的动力学特性. 物理学报, 2021, 70(23): 230309. doi: 10.7498/aps.70.20211576
    [7] 姜聪颖, 孙飞, 冯子力, 刘世炳, 石友国, 赵继民. 三重简并拓扑半金属磷化钼的时间分辨超快动力学. 物理学报, 2020, 69(7): 077801. doi: 10.7498/aps.69.20191816
    [8] 李牮. 基于Yu-Shiba-Rusinov态的拓扑超导理论. 物理学报, 2020, 69(11): 117401. doi: 10.7498/aps.69.20200831
    [9] 向天, 程亮, 齐静波. 拓扑绝缘体中的超快电荷自旋动力学. 物理学报, 2019, 68(22): 227202. doi: 10.7498/aps.68.20191433
    [10] 任志红, 李岩, 李艳娜, 李卫东. 基于量子Fisher信息的量子计量进展. 物理学报, 2019, 68(4): 040601. doi: 10.7498/aps.68.20181965
    [11] 杨超, 陈澍. 淬火动力学中的拓扑不变量. 物理学报, 2019, 68(22): 220304. doi: 10.7498/aps.68.20191410
    [12] 苏耀恒, 陈爱民, 王洪雷, 相春环. 一维自旋1键交替XXZ链中的量子纠缠和临界指数. 物理学报, 2017, 66(12): 120301. doi: 10.7498/aps.66.120301
    [13] 陈菊, 张毅. El-Nabulsi动力学模型下非Chetaev型非完整系统的精确不变量与绝热不变量. 物理学报, 2015, 64(3): 034502. doi: 10.7498/aps.64.034502
    [14] 陈菊, 张毅. El-Nabulsi动力学模型下Birkhoff系统Noether对称性的摄动与绝热不变量. 物理学报, 2014, 63(10): 104501. doi: 10.7498/aps.63.104501
    [15] 陈艳丽, 彭向阳, 杨红, 常胜利, 张凯旺, 钟建新. 拓扑绝缘体Bi2Se3中层堆垛效应的第一性原理研究. 物理学报, 2014, 63(18): 187303. doi: 10.7498/aps.63.187303
    [16] 张毅. 非保守动力学系统Noether对称性的摄动与绝热不变量. 物理学报, 2013, 62(16): 164501. doi: 10.7498/aps.62.164501
    [17] 车俊岭, 张好, 冯志刚, 张临杰, 赵建明, 贾锁堂. 70S超冷Cs Rydberg原子的动力学演化. 物理学报, 2012, 61(4): 043205. doi: 10.7498/aps.61.043205
    [18] 孙宇航, 李福利. 单个二能级超冷原子在多个单模腔场间的共振隧穿和光子辐射. 物理学报, 2006, 55(3): 1153-1159. doi: 10.7498/aps.55.1153
    [19] 盛阳, 宁西京. 气相碳原子成笼的动力学模拟. 物理学报, 2004, 53(4): 1039-1043. doi: 10.7498/aps.53.1039
    [20] 熊锦, 牛中奇, 张智明. 原子质心运动的量子效应对光场量子噪声压缩的影响. 物理学报, 2002, 51(10): 2245-2244. doi: 10.7498/aps.51.2245
计量
  • 文章访问数:  7078
  • PDF下载量:  175
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-10-30
  • 修回日期:  2018-12-27
  • 上网日期:  2019-02-01
  • 刊出日期:  2019-02-20

/

返回文章
返回