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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.
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Keywords:
- thermal entanglement /
- tripartite negativity /
- single molecular magnet
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[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 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 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 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
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