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Tavis-Cummings模型中的几何量子失协特性

程景 单传家 刘继兵 黄燕霞 刘堂昆

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Tavis-Cummings模型中的几何量子失协特性

程景, 单传家, 刘继兵, 黄燕霞, 刘堂昆

Geometric quantum discord in Tavis-Cummings model

Cheng Jing, Shan Chuan-Jia, Liu Ji-Bing, Huang Yan-Xia, Liu Tang-Kun
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  • 采用几何量子失协的计算方法,通过改变两原子初始状态、腔内光子数和偶极-偶极相互作用强度,研究了Tavis-Cummings模型中的几何量子失协特性.结果表明:几何量子失协都是随时间周期性振荡的,选取适当的初态可以使两原子一直保持失协状态,增加腔内光子数和偶极相互作用对几何量子失协有积极的影响.
    Quantum entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.
      通信作者: 单传家, scj1122@163.com
    • 基金项目: 国家自然科学基金(批准号:11404108)和湖北省自然科学基金(批准号:2016CFB639)资助的课题.
      Corresponding author: Shan Chuan-Jia, scj1122@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11404108) and the Natural Science Foundation of Hubei Province, China (Grant No. 2016CFB639).
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    Fan K M, Zhang G F 2013 Acta Phys. Sin. 62 130301(in Chinese) [樊开明, 张国锋 2013 物理学报 62 130301]

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    Hu M L, Tian D P 2014 Ann. Phys. 343 132

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  • [1]

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

    [2]

    Bennett C H, Brassard G, Grepean C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895

    [3]

    Shor P W 1992 Phys. Rev. Lett. 52 2493

    [4]

    Bogoliubov N M, Bulloughz R K, Timonenx 1996 J. Phys. A: Math. Gen. 19 6305

    [5]

    Zuo Z C, Xia Y J 2003 Acta Phys. Sin. 52 2687(in Chinese) [左战春, 夏云杰 2003 物理学报 52 2687]

    [6]

    Guo L, Liang X T 2009 Acta Phys. Sin. 58 50(in Chinese) [郭亮, 梁先庭 2009 物理学报 58 50]

    [7]

    Zhang G F, Bu J J 2010 Acta Phys. Sin. 59 1462(in Chinese) [张国锋, 卜晶晶 2010 物理学报 59 1462]

    [8]

    Ollivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017910

    [9]

    Hu Y H, Tan Y G, Liu Q 2013 Acta Phys. Sin. 62 074202(in Chinese) [胡要花, 谭勇刚, 刘强 2013 物理学报 62 074202]

    [10]

    He Z, Li L W 2013 Acta Phys. Sin. 18 180301(in Chinese) [贺志, 李龙武 2013 物理学报 18 180301]

    [11]

    Ali M, Rau A R P, Alber G 2010 Phys. Rev. A 81 359

    [12]

    Dakic B, Vedral V, Brukner C 2010 Phys. Rev. Lett. 105 4649

    [13]

    Fan K M, Zhang G F 2013 Acta Phys. Sin. 62 130301(in Chinese) [樊开明, 张国锋 2013 物理学报 62 130301]

    [14]

    Hu M L, Tian D P 2014 Ann. Phys. 343 132

    [15]

    LI Y J, Liu J M, Zhang Y 2014 Chin. Phys. B 23 110306

    [16]

    Chang L, Luo S 2013 Phys. Rev. A 82 034302

    [17]

    Zhu H J, Zhang G F 2014 Chin. Phys. B 23 120306

    [18]

    Song W, Yu L B, Dong P, Li D C, Yang M, Cao Z L 2013 Sci. China: Phys. Mech. Astron. 56 737

    [19]

    Xiao Y L, Li T, Fei S M, Jing N, Wang Z X 2016 Chin. Phys. B 25 030301

    [20]

    Zou H M, Fang M F 2016 Chin. Phys. B 25 090302

    [21]

    Shan C J, Xia Y J 2006 Acta Phys. Sin. 55 1585(in Chinese) [单传家, 夏云杰 2006 物理学报 55 1585]

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出版历程
  • 收稿日期:  2017-12-20
  • 修回日期:  2018-03-14
  • 刊出日期:  2018-06-05

Tavis-Cummings模型中的几何量子失协特性

  • 1. 湖北师范大学物理与电子科学学院, 黄石 435002
  • 通信作者: 单传家, scj1122@163.com
    基金项目: 国家自然科学基金(批准号:11404108)和湖北省自然科学基金(批准号:2016CFB639)资助的课题.

摘要: 采用几何量子失协的计算方法,通过改变两原子初始状态、腔内光子数和偶极-偶极相互作用强度,研究了Tavis-Cummings模型中的几何量子失协特性.结果表明:几何量子失协都是随时间周期性振荡的,选取适当的初态可以使两原子一直保持失协状态,增加腔内光子数和偶极相互作用对几何量子失协有积极的影响.

English Abstract

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