考虑DM相互作用的Ising系统中量子失协的含时演化

J4 ›› 2012, Vol. 29 ›› Issue (5): 547-554.

考虑DM相互作用的Ising系统中量子失协的含时演化

郭战营^1,2, 肖瑞华¹, 方建兴¹

1苏州大学物理科学与技术学院，江苏苏州 215006;
2 焦作师范高等专科学校物理系，河南焦作 454001

收稿日期:2011-07-04 修回日期:2011-09-16 出版日期:2012-09-28 发布日期:2012-09-02
通讯作者: 方建兴(1963-)，博士生导师，教授，主要研究方向为量子信息学。 E-mail:fangjx@suda.edu.cn
作者简介:郭战营(1970-)，硕士，副教授，主要研究量子失协及纠缠。E-mail:guo7011@126.com
基金资助:
国家自然科学基金资助项目（11074184），河南省高校青年骨干教师资助计划项目(2009GGJS-163)

Dynamics of quantum discord for Ising system with Dzialoshinskii-Moriya interaction

GUO Zhan-ying^1,2, XIAO Rui-hua¹, FANG Jian-xing¹?

1 School of Physical Science and Technology, Soochow University, Suzhou 215006, China;
2 Department of Physics, Jiaozuo Normal College, Jiaozuo 454001, China

Received:2011-07-04 Revised:2011-09-16 Published:2012-09-28 Online:2012-09-02

摘要/Abstract

摘要：

研究了处在非均匀磁场中的两粒子Ising系统，在考虑DM相互作用情况下，其量子失协（QD）随时间演化问题。对于初始处于Werner态的系统，详细分析了在随时间演化过程中DM相互作用、不均匀磁场的不均匀度、初态的纯度等因素对量子失协和量子纠缠的影响。通过比较可以发现，两者在很大程度上保持着相似的变化规律，最明显的不同在于演化过程中，在有限的时间内量子失协并不会消失，但是量子纠缠却会出现突然死亡现象（ESD）。这一明显不同的特征表明量子失协比量子纠缠具有更大的应用空间，通过控制外部条件，可以很好的控制量子失协随时间的演化过程。

关键词: 量子光学, 量子失协, 含时演化, Ising 系统, DM相互作用

Abstract:

The dynamics of quantum discord (QD) is investigated in the two-qubit Ising system in an inhomogeneous magnetic field with the Dzialoshinskii-Moriya (DM) interaction. The system is initially prepared in the Werner state，and the effects of the DM interaction, the degree of inhomogeneous magnetic field and the purity of the initial state on QD and the entanglement in the evolution process are analyzed in detail. By a comparison, it is found that both the quantum discord and the entanglement take similar behaviors to a large extent, and QD does not vanish in the finite time, but the phenomenon of the entanglement sudden death (ESD) appears during the evolution process. This is an interesting difference, which shows that the quantum discord is more practical than the entanglement to evaluate the quantum correlation. These effects also indicate that one can control the quantum discord of the system by some exterior conditions.

Key words: quantum optics, quantum discord, dynamics, Ising system, DM interaction

中图分类号:

O431.2

郭战营肖瑞华方建兴. 考虑DM相互作用的Ising系统中量子失协的含时演化[J]. J4, 2012, 29(5): 547-554.

GUO Zhan-ying, XIAO Rui-hua, FANG Jian-Xing? . Dynamics of quantum discord for Ising system with Dzialoshinskii-Moriya interaction[J]. J4, 2012, 29(5): 547-554.

参考文献

[1] Bennett C H, et a1. Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states[J]. Phys.Rev.Lett., 1992, 69: 2881-2884.
[2] Nielsen M A and Chuang I L, Quantum Computation and Quantum Information[M], Cambridge University Press, Cambridge (2000).
[3] Datta A, F lammia S T , and Caves C M, Entanglement and the power of one qubit[J]. Phys. Rev. A, 2005, 72: 042316.
[4] Datta A, Shaji A, and Caves C M, Quantum discord and the power of one qubit[J]. Phys. Rev. Lett. 2008, 100: 050502.
[5] Lanyon B P, Barbieri M, Almeida M P, et al. Experimental quantum computing without entanglement[J].Phys. Rev. Lett. 2008, 101: 200501.
[6] Ollivier H and Zurek W H, Quantum discord:A measure of the quantumness of correlations[J]. Phys. Rev. Lett. 2001, 88: 017901.
[7] Zurek W H, Quantum discord and Maxwell’s demons[J]. Phys. Rev. A, 2003, 67: 012320.
[8] Henderson L and Vedral V, Classical quantum and total correlations[J].J. Phys. A 2001, 34: 6899.
[9] Dillenschneider R and Lutz E, Energetics of quantum correlations[J]. Euro. Phys. Lett., 2009, 88:50003.
[10] Dillenschneider R, Quantum discord and quantum phase transition in spin chains[J]. Phys. Rev. B, 2008, 78: 224413.
[11] Sarandy M S, Classical correlation and quantum discord in critical systems[J].Phys. Rev. A, 2009, 80: 022108.
[12] Zurek W H, Decoherence, einselection, and the quantum origins of the classical [J]. Rev. Mod. Phys. 2003, 75: 715.
[13] Bellomo B, Rranco R L, Compagno G, Non-Markovian effects on the dynamics of entanglement[J].Phys. Rev. Lett. 2007, 99: 160502.
[14] Bellomo B, Franco R L, Compagno G, Entanglement dynamics of two independent qubits in environments with and without memory[J]. Phys. Rev. A, 2008, 77: 032342.
[15] Bellomo B, Franco R L, Giuseppe Compagno,Entanglement trapping in structured environments[J]. Phys. Rev. A, 2008, 78: 062309.
[16] Bellomo B, Franco R L, Maniscalco S, et al., Entanglement trapping in structured environments[J]. Phys. Rev. A, 2008, 78: 060302(R).
[17] Wang B, Xu Z Y, Chen Z Q, et al., Non-Markovian effect on the quantum discord[J]. Phy. Rev. A, 2010, 81: 014101.
[18] Mazzola L, Piilo J, Maniscalco S, Sudden transition between classical and quantum decoherence[J]. Phys. Rev. Lett., 2010, 104: 200401.
[19] Fanchini F F, Werlang T, Brasil C A, et al., Non-Markovian dynamics of quantu m discord[J]. Phys. Rev. A, 2010, 81: 052107.
[20] Yu T, Eberly J H, Finite-time disentanglement via spontaneous emission[J]. Phys. Rev. Lett., 2004, 93: 140404.
[21] Yu T, Eberly J H, Sudden death of entanglement[J].Science, 2009, 323: 598.
[22] Lombardo F C, Villar P I, Environmentally induced effects on a bipartite two-level system: Geometric phase and entanglement properties[J]. Phys. Rev. A, 2010, 81: 022115.
[23] Hu X and Sarma S D, Hilbert-space structure of a solid-state quantum computer: Two-electron states of a double-quantum-dot artificial molecule[J]. Phys. Rev. A, 2000, 61: 062301.
[24] Hu X, Sousa R d, and Sarma S D, Interplay between Zeeman coupling and swap action in spin-based quantum computer models: error correction in inhomogeneous magnetic fields[J]. Phys. Rev. Lett. , 2001, 86: 918-921.
[25] Makhlin Y, Sch n G, and Shnirman A, Quantum-state engineering with Josephson-junction devices[J]. Rev. Mod. Phys., 2001, 73: 357.
[26]Chen Wei. Thermal entanglement of XXZ model under magnetic field[J].Chinese Journal of Quantum Electronics (量子电子学报),2008,25:177-180.
[27]Qin Meng, et al. Entanglement in spin-1 Heisenberg XXZ chain[J]. Chinese Journal of Quantum Electronics (量子电子学报),2008,25: 302-306.
[28] Werlang T and Rigolin G, Thermal and magnetic quantum discord in Heisenberg models[J]. Phys. Rev. A, 2010, 81: 044101.
[29] Wang Q, Liao J Q and Zeng H S, General: quantum thermal discord in a two-spin-1/2 XXZ model[J].Chin.Phys. B , 2010, 19: 100311.
[30]Cai Z, Lu W B: Effects of the staggered Dzyaloshinskii-Moriya interaction on entanglement in antiferromagnetic Heisenberg chain[J]. Acta Phys. Sin., 2008, 57: 7267 (In Chinese).
[31]Ma X S, Thermal entanglemment of a two-qutrit XX chain with Dzialoshinski-Moriya interaction[J].Opt. Commun., 2008, 218: 484.
[32]Hu J, Fang J X, Qian L,et al., Thermal entanglement of Ising Model with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2011, 28: 329-334.
[33] Hill S and Wootters W K, Entanglement of a pair of quantum bits[J]. Phys. Rev. Lett., 1997, 78: 5022.