{Cu3}单分子磁体在磁场中的热纠缠

李纪强; 成志; 周斌

doi:10.7498/aps.62.190302

摘要

本文研究单分子磁体Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O中三角自旋环在磁场作用下的热纠缠性质, 利用数值计算求出任意两个Cu2+离子量子比特之间的配对纠缠度, 分别记为C12, C23和C13. 研究结果表明, 磁场的方向和大小以及温度对配对纠缠度具有重要影响, 而且参数的变化对C12, C23和C13的影响也是各不相同. 给出外加三个不同方向的磁场时, 配对纠缠度C12, C23和C13各自对应的临界温度Tc随磁场强度的变化图, 由此可以得到单分子磁体三角自旋环中存在纠缠态的参数范围. 通过选择适当的磁场方向和大小以及温度等实验参数, 可以有效地调节和提高单分子磁体中的配对纠缠度.

关键词:

Abstract

We have investigated the properties of thermal entanglement in a triangular spin ring of the single molecular magnet (SMM) Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O in a magnetic field, and the pairwise concurrences of arbitrary two Cu2+ ion qubits are calculated numerically, hereafter abbreviated as C12, C23 and C13, respectively. Results show that the magnitude and direction of magnetic field as well as temperature have important effects on the pairwise thermal entanglement. Moreover, C12, C23 and C13 have difference variations with the change of the parameters. We also plot the changes of the critical temperatures Tc of C12, C23 and C13 with the magnetic fields along three different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the ranges of parameters in which the pairwise thermal entanglement in a triangular spin ring of the SMM exists. Therefore, the pairwise entanglement can be controlled and enhanced in the SMM by choosing appropriate magnitude and direction of magnetic field and temperature.

Keywords:

作者及机构信息

1.
湖北大学物理学与电子技术学院, 武汉 430062

基金项目: 国家自然科学基金(批准号:11274102)和教育部新世纪优秀人才支持计划(批准号:NCET-11-0960)资助的课题.

Authors and contacts

1.
School of Physics and Electronic Technology, Hubei University, Wuhan 430062, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274102), and the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960).

参考文献

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施引文献

[1]	Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[2]	Wang X G 2001 Phys. Rev. A 64 012313
[3]	Wang X G 2001 Phys. Lett. A 281 101
[4]	Wang X G 2002 Phys. Rev. A 66 034302
[5]	Zhang G F, Li S S 2005 Phys. Rev. A 72 034302
[6]	Sun Y, Chen Y, Chen H 2003 Phys. Rev. A 68 044301
[7]	Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张英丽, 周斌 2011 60 120301]
[8]	Xi X Q, Chen W X, Liu Q, Yue R H 2006 Acta Phys. Sin. 55 3026 (in Chinese) [惠小强, 陈文学, 刘起, 岳瑞宏 2006 55 3026]
[9]	Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311
[10]	Wu K D, Zhou B, Cao W Q 2007 Phys. Lett. A 362 381
[11]	Cao M, Zhu S Q 2006 Chin. Phys. Lett. 23 2888
[12]	Li D C, Wang X P, Cao Z L 2008 J. Phys.: Condens. Matter 20 325229
[13]	Pan H Z, Kuang L M 2004 Chin. Phys. Lett. 21 424
[14]	Xi X Q, Chen W X, Yue R H 2002 Chin. Phys. Lett. 19 1044
[15]	Lu P, Wang J S 2009 Acta Phys. Sin. 58 5955 (in Chinese) [卢鹏, 王顺金 2009 58 5955]
[16]	Ren J Z, Shao X Q, Zhang S, Yeon K H 2010 Chin. Phys. B 19 100307
[17]	Zhou L, Song H S, Guo Y Q, Li C 2003 Phys. Rev. A 68 024301
[18]	Zhang T, Xi X Q, Yue R H 2004 Acta Phys. Sin. 53 2755 (in Chinese) [张涛, 惠小强, 岳瑞宏 2004 53 2755]
[19]	Wang Y H, Xia Y J 2009 Acta Phys. Sin. 58 7479 (in Chinese) [王彦辉, 夏云杰 2009 58 7479]
[20]	Hu Z N, Yi K S, Park K S 2007 J. Phys. A: Math. Theor. 40 7283
[21]	Luczak J, Bulka B R 2012 J. Phys.: Condens. Matter 24 375303
[22]	Zhou B 2011 Int. J. Mod. Phys. B 25 2135
[23]	Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313
[24]	Qin M, Tian D P, Tao Y J 2008 Acta Phys. Sin. 57 5395 (in Chinese) [秦猛, 田东平, 陶应娟 2008 57 5395]
[25]	Zheng Q, Zhang X P, Zhi Q J, Ren Z Z 2009 Chin. Phys. B 18 3210
[26]	Thomas L, Lionti F, Ballou R, Gatteschi D, Sessoli R, Barbara B 1996 Nature 383 145
[27]	Wernsdorfer W, Sessoli R 1999 Science 284 133
[28]	Kortz U, Nellutla S, Stowe A C, Dalal N S, Rauwald U, Danquah W, Ravot D 2004 Inorg. Chem. 43 2308
[29]	Stowe A C, Nellutla S, Dalal N S, Kortz U 2004 Eur. J. Inorg. Chem. 19 3792
[30]	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
[31]	Bogani L, Wernsdorfer W 2008 Nature Mater. 7 179
[32]	Leuenberger M N, Loss D 2001 Nature 410 789
[33]	Zhou B, Tao R B, Shen S Q, Liang J Q 2002 Phys. Rev. A 66 010301
[34]	Meier F, Levy J, Loss D 2003 Phys. Rev. B 68 134417
[35]	Troiani F, Ghirri A, Affronte M, Carretta S, Santini P, Amoretti G, Piligkos S, Timco G, Winpenny R E P 2005 Phys. Rev. Lett. 94 207208
[36]	Lehmann J, Gaita-Ariño A, Coronado E, Loss D 2007 Nature Nanotech. 2 312
[37]	Trif M, Troiani F, Stepanenko D, Loss D 2008 Phys. Rev. Lett. 101 217201
[38]	Kortz U, Al-Kassem N K, Savelieff M G, Kadi N A A, Sadakane M 2001 Inorg. Chem. 40 4742
[39]	Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[40]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[41]	Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306

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