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

{Cu3}单分子磁体在热平衡和磁场作用下的三体纠缠

郑一丹 周斌

引用本文:
Citation:

{Cu3}单分子磁体在热平衡和磁场作用下的三体纠缠

郑一丹, 周斌

Tripartite entanglement of {Cu3} single molecular magnet with magnetic field in thermal equilibrium

Zheng Yi-Dan, Zhou Bin
PDF
导出引用
  • 本文研究了Na9[Cu3Na3(H2O)9(-AsW9O33)2] 26H2O (简记为{Cu3})单分子磁体在热平衡和外加磁场作用下的三体纠缠性质, 利用等效自旋模型和实验拟合参数, 数值计算了{Cu3}型三角自旋环中三体负性纠缠度 (tripartite negativity). 分别考虑沿垂直于三角自旋环方向的磁场、平行于三角自旋环方向的磁场, 以及倾斜磁场的情形. 结果表明, 磁场的方向、大小以及温度对系统三体负性纠缠度有着重要影响. 文中给出了在不同磁场方向下, 临界温度随磁场强度的变化图, 由此可以得到三体纠缠存在的参数区域. 同时发现在特定的参数区域, 该系统存在纠缠恢复现象. 因此适当调节温度、磁场强度大小和磁场方向可以有效调控{Cu3}型三角自旋环中的三体纠缠性质.
    Quantum entanglement is one of the most fundamental properties of quantum mechanics. Because of the nonlocality, quantum entanglement is widely used in quantum computation and quantum information. Considering the fact that thermal fluctuation suppresses quantum effects, the concept of thermal entanglement is introduced to refer to the idea that the effect of temperature should be viewed as external control in the preparation of entangled state. It has been found that nanoscale single molecular magnet has a novel quantum effect at low temperature. Furthermore, single-molecular magnet is viewed as a promising candidate for realizing encoding and manipulation of quantum information. Na9[Cu3Na3(H2O)9(-AsW9O33)2]26H2O (denoted as {Cu3} for convenience) is one of the typical representatives of nanoscale single molecular magnets. In this paper, we will theoretically analyze the properties of tripartite entanglement in {Cu3} with an external magnetic field in thermal equilibrium. The tripartite negativity is used to characterize the tripartite entanglement. The tripartite negativity of {Cu3} single molecular magnet is calculated numerically by using the equivalent spin model and experimental fitting parameters. We consider the magnetic fields along the vertical and the parallel directions of triangular spin ring, respectively, and the case with a tilted magnetic field is also discussed in this paper. It is shown that the magnitude and direction of magnetic field, and temperature have importance effects on the tripartite negativity of the system. It is found that the larger extra strong magnetic field will inhibit the generation of the quantum state of tripartite entanglement at higher temperature. In addition, compared with the magnetic field along the parallel direction of triangular spin ring and the tilted magnetic field, the magnetic field along the vertical direction of triangular spin ring obtains larger values of tripartite negativity under the same temperature and magnetic field. We also plot the variations of the critical temperature with the magnetic field along different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the range of parameters in which the tripartite entanglement of the system exists. We also find that entanglement revival behaviors may occur in the specific range of parameters. Therefore, the properties of the tripartite entanglement in the {Cu3} triangular spin ring can be controlled and enhanced by choosing appropriate magnitude and direction of the magnetic field and temperature.
      通信作者: 周斌, binzhou@hubu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11274102)、教育部新世纪优秀人才支持计划(批准号: NCET-11-0960)和高等学校博士学科点专项科研基金(批准号: 20134208110001)资助的课题.
      Corresponding author: Zhou Bin, binzhou@hubu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
    [1]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881

    [2]

    Schumacher B 1995 Phys. Rev. A 51 2738

    [3]

    Mattle K, Weinfurter H, Kwiat P G, Zeilinger Z 1996 Phys. Rev. Lett. 76 4656

    [4]

    Bennett C H 1993 Phys. Rev. Lett. 70 1895

    [5]

    Kim Y H, Kulik S P, Shih Y 2001 Phys. Rev. Lett. 86 1370

    [6]

    Ekert A K 1991 Phys. Rev. Lett. 67 661

    [7]

    Deutsch D, Ekert A, Jozsa R, Macchiavello C, Popescu S S 1996 Phys. Rev. Lett. 77 2818

    [8]

    Wang X G 2001 Phys. Rev. A 64 012313

    [9]

    Wang X G 2001 Phys. Lett. A 281 101

    [10]

    Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张英丽, 周斌 2011 物理学报 60 120301]

    [11]

    Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311

    [12]

    Wang X G, Fu H C, Solomon A I 2001 J. Phys. A 34 11307

    [13]

    Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313

    [14]

    Ma X S, Qiao Y, Cheng M T, Liu X D 2014 Quantum Inf. Process. 13 1879

    [15]

    Xu S, Song X K, Ye L 2014 Quantum Inf. Process. 13 1013

    [16]

    Guo K T, Liang M C, Xu H Y, Zhu C B 2010 J. Phys. A 43 505301

    [17]

    Sun Z, Wang X G, Hu A Z, Li Y Q 2006 Physica A 370 483

    [18]

    Sabn C, Garca-Alcaine G 2008 Eur. Phys. J. D 48 435

    [19]

    Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306

    [20]

    Yu C S, Song H S 2004 Phys. Lett. A 330 377

    [21]

    Meyer D, Wallach N R 2002 J. Math. Phys. 43 4273

    [22]

    Brennen G K 2003 Quantum Inf. Comput. 3 619

    [23]

    Love P J, van den Brink A M, Smirnov A Y, Amin M H S, Grajcar M, ll'ichev E, lzmalkov A, Zagoskin A M 2007 Quantum Inf. Process. 6 187

    [24]

    Ma X S, Zhao G X, Zhang J Y, Wang A M 2013 Quantum Inf. Process. 12 321

    [25]

    Anz F, Militello B, Messina A 2010 J. Phys. B 43 205501

    [26]

    Guo Y N, Fang M F, Zhang S Y, Liu X 2015 Phys. Scr. 90 035103

    [27]

    Feng L J, Zhang Y J, Zhang L, Xia Y J 2015 Chin. Phys. B 24 110305

    [28]

    Li Y J, Liu J M 2014 Acta Phys. Sin. 63 200302 (in Chinese) [李艳杰, 刘金明 2014 物理学报 63 200302]

    [29]

    Cai J T, Abliz A 2013 Phys. A 392 2607

    [30]

    Weinstein Y S 2009 Phys. Rev. A 79 012318

    [31]

    Buscemi F, Bordone P 2011 Phys. Rev. A 84 022303

    [32]

    Friedman J R, Sarachik M P, Tejada J, Ziolo R 1996 Phys. Rev. Lett. 76 3830

    [33]

    Thomas L, Lionti F, Ballou R, Gatteschi D, Sessoli R, Barbara B 1996 Nature 383 145

    [34]

    Wernsdorfer W, Sessoli R 1999 Science 284 133

    [35]

    Ardavan A, Rival O, Morton J J L, Blundell S J, Tyryshkin A M, Timco G A, Winpenny R E P 2007 Phys. Rev. Lett. 98 057201

    [36]

    Kortz U, Nellutla S, Stowe A C, Dalal N S, Rauwald U, Danquah W, Ravot D 2004 Inorg. Chem. 43 2308

    [37]

    Stowe A C, Nellutla S, Dalal N S, Kortz U 2004 Eur. J. Inorg. Chem. 2004 3792

    [38]

    Choi K Y, Matsuda Y H, Nojiri H, Kortz U, Hussain F, Stowe A C, Ramsey C, Dalal N S 2006 Phys. Rev. Lett. 96 107202

    [39]

    Islam M F, Nossa J F, Canali C M 2010 Phys. Rev. B 82 155446

    [40]

    Mousolou V A, Canali C M, Sjqvist E 2015 arXiv:1512.01636v1[quant-ph]

    [41]

    Li J Q, Cheng Z, Zhou B 2013 Acta Phys. Sin. 62 190302 (in Chinese) [李纪强, 成志, 周斌 2013 物理学报 62 190302]

    [42]

    Li J Q, Zhou B 2014 Chin. Phys. B 23 070302

    [43]

    Vidal G, Werner R F 2002 Phys. Rev. A 65 032314

  • [1]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881

    [2]

    Schumacher B 1995 Phys. Rev. A 51 2738

    [3]

    Mattle K, Weinfurter H, Kwiat P G, Zeilinger Z 1996 Phys. Rev. Lett. 76 4656

    [4]

    Bennett C H 1993 Phys. Rev. Lett. 70 1895

    [5]

    Kim Y H, Kulik S P, Shih Y 2001 Phys. Rev. Lett. 86 1370

    [6]

    Ekert A K 1991 Phys. Rev. Lett. 67 661

    [7]

    Deutsch D, Ekert A, Jozsa R, Macchiavello C, Popescu S S 1996 Phys. Rev. Lett. 77 2818

    [8]

    Wang X G 2001 Phys. Rev. A 64 012313

    [9]

    Wang X G 2001 Phys. Lett. A 281 101

    [10]

    Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张英丽, 周斌 2011 物理学报 60 120301]

    [11]

    Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311

    [12]

    Wang X G, Fu H C, Solomon A I 2001 J. Phys. A 34 11307

    [13]

    Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313

    [14]

    Ma X S, Qiao Y, Cheng M T, Liu X D 2014 Quantum Inf. Process. 13 1879

    [15]

    Xu S, Song X K, Ye L 2014 Quantum Inf. Process. 13 1013

    [16]

    Guo K T, Liang M C, Xu H Y, Zhu C B 2010 J. Phys. A 43 505301

    [17]

    Sun Z, Wang X G, Hu A Z, Li Y Q 2006 Physica A 370 483

    [18]

    Sabn C, Garca-Alcaine G 2008 Eur. Phys. J. D 48 435

    [19]

    Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306

    [20]

    Yu C S, Song H S 2004 Phys. Lett. A 330 377

    [21]

    Meyer D, Wallach N R 2002 J. Math. Phys. 43 4273

    [22]

    Brennen G K 2003 Quantum Inf. Comput. 3 619

    [23]

    Love P J, van den Brink A M, Smirnov A Y, Amin M H S, Grajcar M, ll'ichev E, lzmalkov A, Zagoskin A M 2007 Quantum Inf. Process. 6 187

    [24]

    Ma X S, Zhao G X, Zhang J Y, Wang A M 2013 Quantum Inf. Process. 12 321

    [25]

    Anz F, Militello B, Messina A 2010 J. Phys. B 43 205501

    [26]

    Guo Y N, Fang M F, Zhang S Y, Liu X 2015 Phys. Scr. 90 035103

    [27]

    Feng L J, Zhang Y J, Zhang L, Xia Y J 2015 Chin. Phys. B 24 110305

    [28]

    Li Y J, Liu J M 2014 Acta Phys. Sin. 63 200302 (in Chinese) [李艳杰, 刘金明 2014 物理学报 63 200302]

    [29]

    Cai J T, Abliz A 2013 Phys. A 392 2607

    [30]

    Weinstein Y S 2009 Phys. Rev. A 79 012318

    [31]

    Buscemi F, Bordone P 2011 Phys. Rev. A 84 022303

    [32]

    Friedman J R, Sarachik M P, Tejada J, Ziolo R 1996 Phys. Rev. Lett. 76 3830

    [33]

    Thomas L, Lionti F, Ballou R, Gatteschi D, Sessoli R, Barbara B 1996 Nature 383 145

    [34]

    Wernsdorfer W, Sessoli R 1999 Science 284 133

    [35]

    Ardavan A, Rival O, Morton J J L, Blundell S J, Tyryshkin A M, Timco G A, Winpenny R E P 2007 Phys. Rev. Lett. 98 057201

    [36]

    Kortz U, Nellutla S, Stowe A C, Dalal N S, Rauwald U, Danquah W, Ravot D 2004 Inorg. Chem. 43 2308

    [37]

    Stowe A C, Nellutla S, Dalal N S, Kortz U 2004 Eur. J. Inorg. Chem. 2004 3792

    [38]

    Choi K Y, Matsuda Y H, Nojiri H, Kortz U, Hussain F, Stowe A C, Ramsey C, Dalal N S 2006 Phys. Rev. Lett. 96 107202

    [39]

    Islam M F, Nossa J F, Canali C M 2010 Phys. Rev. B 82 155446

    [40]

    Mousolou V A, Canali C M, Sjqvist E 2015 arXiv:1512.01636v1[quant-ph]

    [41]

    Li J Q, Cheng Z, Zhou B 2013 Acta Phys. Sin. 62 190302 (in Chinese) [李纪强, 成志, 周斌 2013 物理学报 62 190302]

    [42]

    Li J Q, Zhou B 2014 Chin. Phys. B 23 070302

    [43]

    Vidal G, Werner R F 2002 Phys. Rev. A 65 032314

  • [1] 毛丽君, 张云波. 三量子比特Dicke模型中的两体和三体纠缠动力学. 物理学报, 2021, 70(4): 040301. doi: 10.7498/aps.70.20201602
    [2] 刘贵艳, 毛竹, 周斌. 具有次近邻相互作用的五量子比特XXZ海森伯自旋链的热纠缠. 物理学报, 2018, 67(2): 020301. doi: 10.7498/aps.67.20171641
    [3] 郑一丹, 毛竹, 周斌. 具有三角自旋环的伊辛-海森伯链的热纠缠. 物理学报, 2017, 66(23): 230304. doi: 10.7498/aps.66.230304
    [4] 刘世右, 郑凯敏, 贾芳, 胡利云, 谢芳森. 单-双模组合压缩热态的纠缠性质及在量子隐形传态中的应用. 物理学报, 2014, 63(14): 140302. doi: 10.7498/aps.63.140302
    [5] 李纪强, 成志, 周斌. {Cu3}单分子磁体在磁场中的热纠缠. 物理学报, 2013, 62(19): 190302. doi: 10.7498/aps.62.190302
    [6] 卢道明. 耦合腔系统中的三体纠缠演化. 物理学报, 2012, 61(18): 180301. doi: 10.7498/aps.61.180301
    [7] 叶骞, 陈千帆, 范洪义. 利用热纠缠态表象获得Caldeira-Leggett密度算符方程的积分形式解. 物理学报, 2012, 61(21): 210301. doi: 10.7498/aps.61.210301
    [8] 胡要花. Stark位移对热环境下双Jaynes-Cummings模型中原子纠缠的影响. 物理学报, 2012, 61(16): 160304. doi: 10.7498/aps.61.160304
    [9] 王鲁顺, 江慧, 孔祥木. 混合自旋XY系统热纠缠的研究. 物理学报, 2012, 61(24): 240304. doi: 10.7498/aps.61.240304
    [10] 姜春蕾, 刘晓娟, 刘明伟, 王艳辉, 彭朝晖. 内禀退相干下海森伯XY模型中的热纠缠性质及其相干调控. 物理学报, 2012, 61(17): 170302. doi: 10.7498/aps.61.170302
    [11] 张英丽, 周斌. 具有Dzyaloshinskii-Moriya相互作用的四量子比特海森堡XXZ模型中的热纠缠. 物理学报, 2011, 60(12): 120301. doi: 10.7498/aps.60.120301
    [12] 刘圣鑫, 李莎莎, 孔祥木. Dzyaloshinskii-Moriya相互作用对量子XY链中热纠缠的影响. 物理学报, 2011, 60(3): 030303. doi: 10.7498/aps.60.030303
    [13] 冯海冉, 李鹏, 郑雨军, 丁世良. 用李代数方法解析研究线性三原子分子振动的动力学纠缠. 物理学报, 2010, 59(8): 5246-5250. doi: 10.7498/aps.59.5246
    [14] 马海强, 王素梅, 吴令安. 基于偏振纠缠光子对的单光子源. 物理学报, 2009, 58(2): 717-721. doi: 10.7498/aps.58.717
    [15] 杜秀梅, 满忠晓, 夏云杰. 外磁场下XY模型中两量子位热纠缠的性质及其调控研究. 物理学报, 2008, 57(12): 7457-7462. doi: 10.7498/aps.57.7457
    [16] 秦 猛, 田东平, 陶应娟. 自旋为1的三粒子Heisenberg XXX链中杂质对热纠缠的影响. 物理学报, 2008, 57(9): 5395-5399. doi: 10.7498/aps.57.5395
    [17] 向少华, 杨 雄, 宋克慧. 推广的Jaynes-Cummings模型中原子纠缠的时间演化和热纠缠态. 物理学报, 2004, 53(5): 1289-1292. doi: 10.7498/aps.53.1289
    [18] 张 涛, 惠小强, 岳瑞宏. 三量子位Heisenberg XX 链中杂质对纠缠的影响. 物理学报, 2004, 53(8): 2755-2760. doi: 10.7498/aps.53.2755
    [19] 左战春, 夏云杰. Tavis-Cummings模型中三体纠缠态纠缠量的演化特性. 物理学报, 2003, 52(11): 2687-2693. doi: 10.7498/aps.52.2687
    [20] 石名俊, 杜江峰, 朱栋培. 量子纯态的纠缠度. 物理学报, 2000, 49(5): 825-829. doi: 10.7498/aps.49.825
计量
  • 文章访问数:  3181
  • PDF下载量:  266
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-03-21
  • 修回日期:  2016-04-14
  • 刊出日期:  2016-06-05

{Cu3}单分子磁体在热平衡和磁场作用下的三体纠缠

  • 1. 湖北大学物理与电子科学学院, 武汉 430062
  • 通信作者: 周斌, binzhou@hubu.edu.cn
    基金项目: 国家自然科学基金(批准号: 11274102)、教育部新世纪优秀人才支持计划(批准号: NCET-11-0960)和高等学校博士学科点专项科研基金(批准号: 20134208110001)资助的课题.

摘要: 本文研究了Na9[Cu3Na3(H2O)9(-AsW9O33)2] 26H2O (简记为{Cu3})单分子磁体在热平衡和外加磁场作用下的三体纠缠性质, 利用等效自旋模型和实验拟合参数, 数值计算了{Cu3}型三角自旋环中三体负性纠缠度 (tripartite negativity). 分别考虑沿垂直于三角自旋环方向的磁场、平行于三角自旋环方向的磁场, 以及倾斜磁场的情形. 结果表明, 磁场的方向、大小以及温度对系统三体负性纠缠度有着重要影响. 文中给出了在不同磁场方向下, 临界温度随磁场强度的变化图, 由此可以得到三体纠缠存在的参数区域. 同时发现在特定的参数区域, 该系统存在纠缠恢复现象. 因此适当调节温度、磁场强度大小和磁场方向可以有效调控{Cu3}型三角自旋环中的三体纠缠性质.

English Abstract

参考文献 (43)

目录

    /

    返回文章
    返回