非均匀海森堡XY周期性链的纠缠

J4 ›› 2012, Vol. 29 ›› Issue (4): 448-456.

非均匀海森堡XY周期性链的纠缠

朱士群, 程明

苏州大学物理科学与技术学院，苏州，江苏 215006

收稿日期:2011-06-30 修回日期:2011-08-20 出版日期:2012-07-28 发布日期:2012-07-01
通讯作者: 朱士群(1950-),江苏徐州人，博士，教授，博导，主要研究量子光学与量子信息，激光物理与随机过程，非线性光学与复杂网络等。 E-mail:szhu@suda.edu.cn
基金资助:
国家自然科学基金（11074184）

Entanglement of Heisenberg XY model on inhomogeneous periodic chain

CHENG Ming, ZHU Shiqun

School of Physical Science and Technology, Soochow University, Suzhou 215006, China

Received:2011-06-30 Revised:2011-08-20 Published:2012-07-28 Online:2012-07-01

摘要/Abstract

摘要：

研究了各向同性海森堡XY链在非均匀磁场中纠缠的含时演化以及热纠缠的问题。纠缠在量子信息领域是个十分重要的资源，关于纠缠的度量和含时演化的研究就非常必要。我们主要对共生纠缠度进行了理论计算，通过数值模拟进行了分析。如果外磁场很小，最近邻耦合系数很大，共生纠缠度就在0和1之间振荡。如果外磁场很大，最近邻耦合系数很小，共生纠缠度的最大值会变小，甚至会消失。同时，随着海森堡自旋链中自旋数目的增加，纠缠会减小。随着温度的升高，热纠缠会快速的下降。随着外磁场的增加，热纠缠也会下降。只有在系统的非均匀度增加的时候，热纠缠才会增加。

关键词: 量子光学, 非均匀海森堡链, 共生纠缠度, 纠缠演化, 热纠缠, 外磁场

Abstract:

The time evolution of entanglement and thermal entanglement of an isotropic XY model on the inhomogeneous chain is investigated when there is anisotropic magnetic field. Since entanglement is a very important recourse in the field of quantum information, the study of measure and time evolution of entanglement is necessary. We use the quantity of concurrence to theoretically calculate the entanglement, and analyze it by numerical simulations. If the external magnetic field is small and the nearest neighbor coupling is large, the concurrence oscillates between zero and one. If the external magnetic field is large and the nearest neighbor coupling is small, the maximum concurrence can be reduced and even disappears. Meanwhile, the entanglement decreases when the number of spins in the Heisenberg chain increases. The thermal entanglement drops quickly when the temperature increases. It decreases also as the external magnetic field increases. It can be increased if the inhomogeneity of the system is increased.

Key words: quantum optics, inhomogeneous Heisenberg chain, concurrence, time evolution of entanglement, thermal entanglement, external magnetic field

中图分类号:

O431.2

程明, 朱士群. 非均匀海森堡XY周期性链的纠缠[J]. J4, 2012, 29(4): 448-456.

CHENG Ming, ZHU Shiqun. Entanglement of Heisenberg XY model on inhomogeneous periodic chain[J]. J4, 2012, 29(4): 448-456.

参考文献

[1] Bennett C H, Brassard G., Crpeau C, Jozsa R, Peres A, Wootters W K. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels [J]. Phys. Rev. Lett., 1993, 70: 1895.
[2] Zhu Xun, Wang Gan-quan. A new criterion of entanglement of two electrons [J].(一种新的关于两电子纠缠的判据). Chinese Journal of Quantum Electronics (量子电子学报)，2009, 26(3): 297(in Chinese)
[3] Li Chun-xian，Jin Li-juan，Wang Cheng-zhi. Thermal entanglement，mixture and quantum communication in a spin chain [J].(自旋链中的热纠缠、混合度和量子通讯). Chinese Journal of Quantum Electronics (量子电子学报), 2010, 27(1): 51(in Chinese).
[4]Bouwmeester D, Pan J W, Mattle K, Eible M, Weinfurer H and Zeilinger A. Experimental quantum teleportation [J]. Nature, 1997, 390: 575.
[5] Ding Zhiyong, He Juan, Wu Tao. One step for generation of W-class state via superconducting quantum interference devices [J]. (利用超导量子相干装置一步制备w类纠缠态). Chinese Journal of Quantum Electronics(量子电子学报), 2010, 27(3):314 (in Chinese).
[6] Li Dong-mei. Entanglement swapping of tripartite entangled coherent state by linear optics devices [J]. (利用线性光学器件实现三体纠缠相干态的纠缠交换). Chinese Journal of Quantum Electronics(量子电子学报), 2009, 26(4): 446 (in Chinese).
[7] Yang Fei, Cong Shuang. Entanglement detection and measure of quantum systems [J] (量子系统的纠缠探测与纠缠测量). Chinese Journal of Quantum Electronics (量子电子学报)， 2011, 28 (4): 391 (in Chinese).
[8] Nielsen M A and Chuang I L. Quantum Computation and Quantum Information [M] (Cambridge University Press, Cambridge, UK, 2000).
[9] Kamta G. L, Starace F. Anisotropy and magnetic field effects on the entanglement of a two qubit Heisenberg XY chain [J]. Phys. Rev. Lett., 2002, 88: 107901.
[10] Alcaraz F C, Saguia A, Sarandy M S. Entanglement and quantumpPhases in the anisotropic ferromagnetic Heisenberg chain in the presence of domain walls. quant-ph/0312039.
[11] Dodd P J and Halliwell J J. Disentanglement and decoherence by open system dynamics [J]. Phys. Rev. A, 2004, 69: 052105.
[12] Yu T and Eberly J H. Phonon decoherence of quantum entanglement: Robust and fragile states [J]. Phys. Rev. B, 2002, 66: 193306.
[13] An J-H, Wang S J and Luo H G.. Entanglement production and decoherence-free subspace of two single-mode cavities embedded in a common environment [J]. J. Phys. A: Math. Gen. 2005, 38: 3579
[14] An J-H, Wang S J and Luo H G.. Entanglement dynamics of qubits in a common environment. arXiv:quant-ph/0604020.
[15] Derzhko O, Richter J, Krokhmalskii T, and Zaburannyi O. Regularly alternating spin-1/2 anisotropic XY chains: The ground-state and thermodynamic properties [J]. Phys. Rev. E, 2004, 69: 066112
[16] Derzhko O, Richter J and Zaburannyi O. Quantum spin chains with regularly alternating bonds and fields [J]. Physica A, 2000, 282: 495.
[17] Lima P de, Alves T F A, and Goncalves L L. The isotropic XY model on the inhomogeneous periodic chain [J]. J. Mag. Mag. Mat., 2006, 298: 95.
[18] Wootters W K. Entanglement of formation of an arbitrary state of two qubits [J]. Phys. Rev. Lett, 1998, 80: 2245
[19] Wootters W K. Entanglement of formation and concurrence [J]. Quant. Inf. Comp., 2001. 1: 27.
[20] Lieb E, Schults T, and Mattis D C. Two soluble models of an antiferromagnetic chain [J]. Ann. Phys., 1961, 16:407.