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Dicke模型的量子混沌和单粒子相干动力学特性

宋立军 严冬 盖永杰 王玉波

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Dicke模型的量子混沌和单粒子相干动力学特性

宋立军, 严冬, 盖永杰, 王玉波

Quantum chaos and the dynamic properties of single-particle coherence in Dicke model

Song Li-Jun, Yan Dong, Gai Yong-Jie, Wang Yu-Bo
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  • 量子化的Dicke模型在非旋波近似条件下表现为量子混沌动力学特征.利用单粒子一阶时间关联函数,通过数值计算详细考察了Dicke模型中单粒子相干动力学特性.结果表明:当初始相干态处在混沌区域时,一阶时间关联函数曲线衰减较快,而当初始相干态处在规则区域时,一阶时间关联函数曲线衰减较慢,单粒子相干动力学对初态具有较强的敏感性,经典混沌抑制量子相干. 考察单粒子相干动力学在相空间的平均演化性质,得到一种较好的量子经典对应关系.最后研究了相空间单粒子相干的整体动力学性质,更好地揭示了相空间的混沌和规则结构.
    The Dicke model displays quantum chaotic dynamic properties in the without-rotating-wave approximation. We explore the dynamic properties of the single-particle coherence in Dicke model by using the first-order temporal correlation function and numerical simulation. The results reveal that the first-order temporal correlation function decays very rapidly when the initial coherent state is centered in chaotic regions, but rather slowly when the initial coherent state is centered in regular regions. This indicates that the single-particle coherence is highly sensitive to initial states, and the classical chaos suppresses quantum coherence. The mean single particle coherence during the evolution is studied, and a better quantum-classical correspondence is obtained. Finally, the dynamics of single-particle coherence in the whole phase space is investigated, which reveals the chaotic and regular structures of the phase space more clearly.
    • 基金项目: 国家自然科学基金(批准号: 10947019)和吉林省教育厅科学技术研究计划(批准号:2009237)资助的课题.
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    [2]Heller E J 1984 Phys. Rev. Lett. 53 1515

    [3]

    [3]Schack R, D′Ariano G M, Caves C M 1994 Phys. Rev. E 50 972

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    [4]Lu P, Wang S J 2009 Acta Phys. Sin. 58 5955 (in Chinese) [卢鹏、王顺金 2009 物理学报 58 5955]

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    [5]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]

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    [6]Wang X G, Ghose S, Sanders B C, Hu B 2004 Phys. Rev. E 70 016217

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    [7]Hou X W, Chen J H, Hu B 2005 Phys. Rev. A 71 034302

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    [9]Srensen A 2002 Phys. Rev. A 65 043610

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    ]Kitagawa M, Ueda M 1993 Phys. Rev. A 47 5138

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    ]Song L J, Wang X G, Yan D, Zong Z G 2006 J. Phys. B 39 559

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    ]Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220

    [13]

    ]Yan D, Song L J, Chen D W 2009 Acta Phys. Sin. 58 3679 (in Chinese) [严冬、宋立军、陈殿伟 2009 物理学报 58 3679]

    [14]

    ]Emerson J, Weinstein Y S, Lloyd S, Cory D G 2002 Phys. Rev. Lett. 89 284102

    [15]

    ]Weinstein Y S, Hellberg C S 2005 Phys. Rev. E 71 016209

    [16]

    ]Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623

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    ]Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2006 Phys. Lett. A 353 216

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    ]Zhang D Y, Guo P, Gao F 2007 Acta Phys. Sin. 56 1906 (in Chinese) [张登玉、郭萍、高峰 2007 物理学报 56 1906]

    [19]

    ]Jin G R, Law C K 2008 Phys. Rev. A 78 063620

    [20]

    ]Dicke R H 1954 Phys. Rev. 93 99

    [21]

    ]Furuya K, Nemes M C, Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524

    [22]

    ]Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 661 (in Chinese) [房永翠、杨志安、杨丽云 2008 物理学报 57 661]

    [23]

    ]Zhang W M, Feng D H, Gilmore R 1990 Rev. Mod. Phys. 62 867

    [24]

    ]Shin Y, Sanner C, Jo G B, Pasquini T A, Saba M, Ketterle W, Pritchard D E, Vengalattore M, Prentiss M 2005 Phys. Rev. A 72 021604

    [25]

    ]Chuu C S, Schreck F, Meyrath T P, Hanssen J L, Price G N, Raizen M G 2005 Phys. Rev. Lett. 95 260403

    [26]

    ]Jo G B, Shin Y, Will S, Pasquini T A, Saba M, Ketterle W, Pritchard D E 2007 Phys. Rev. Lett. 98 030407

    [27]

    ]Widera A, Trotzky S, Cheinet P, Folling S, Gerbier F, Bloch I 2008 Phys. Rev. Lett. 100 140401

  • [1]

    [1]Haake F 1991 Quantum Signature of Chaos (Berlin:Springer -Verlag)

    [2]

    [2]Heller E J 1984 Phys. Rev. Lett. 53 1515

    [3]

    [3]Schack R, D′Ariano G M, Caves C M 1994 Phys. Rev. E 50 972

    [4]

    [4]Lu P, Wang S J 2009 Acta Phys. Sin. 58 5955 (in Chinese) [卢鹏、王顺金 2009 物理学报 58 5955]

    [5]

    [5]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]

    [6]

    [6]Wang X G, Ghose S, Sanders B C, Hu B 2004 Phys. Rev. E 70 016217

    [7]

    [7]Hou X W, Chen J H, Hu B 2005 Phys. Rev. A 71 034302

    [8]

    [8]Srensen A, Duan L M, Cirac J I, Zoller P 2001 Nature 409 63

    [9]

    [9]Srensen A 2002 Phys. Rev. A 65 043610

    [10]

    ]Kitagawa M, Ueda M 1993 Phys. Rev. A 47 5138

    [11]

    ]Song L J, Wang X G, Yan D, Zong Z G 2006 J. Phys. B 39 559

    [12]

    ]Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220

    [13]

    ]Yan D, Song L J, Chen D W 2009 Acta Phys. Sin. 58 3679 (in Chinese) [严冬、宋立军、陈殿伟 2009 物理学报 58 3679]

    [14]

    ]Emerson J, Weinstein Y S, Lloyd S, Cory D G 2002 Phys. Rev. Lett. 89 284102

    [15]

    ]Weinstein Y S, Hellberg C S 2005 Phys. Rev. E 71 016209

    [16]

    ]Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623

    [17]

    ]Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2006 Phys. Lett. A 353 216

    [18]

    ]Zhang D Y, Guo P, Gao F 2007 Acta Phys. Sin. 56 1906 (in Chinese) [张登玉、郭萍、高峰 2007 物理学报 56 1906]

    [19]

    ]Jin G R, Law C K 2008 Phys. Rev. A 78 063620

    [20]

    ]Dicke R H 1954 Phys. Rev. 93 99

    [21]

    ]Furuya K, Nemes M C, Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524

    [22]

    ]Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 661 (in Chinese) [房永翠、杨志安、杨丽云 2008 物理学报 57 661]

    [23]

    ]Zhang W M, Feng D H, Gilmore R 1990 Rev. Mod. Phys. 62 867

    [24]

    ]Shin Y, Sanner C, Jo G B, Pasquini T A, Saba M, Ketterle W, Pritchard D E, Vengalattore M, Prentiss M 2005 Phys. Rev. A 72 021604

    [25]

    ]Chuu C S, Schreck F, Meyrath T P, Hanssen J L, Price G N, Raizen M G 2005 Phys. Rev. Lett. 95 260403

    [26]

    ]Jo G B, Shin Y, Will S, Pasquini T A, Saba M, Ketterle W, Pritchard D E 2007 Phys. Rev. Lett. 98 030407

    [27]

    ]Widera A, Trotzky S, Cheinet P, Folling S, Gerbier F, Bloch I 2008 Phys. Rev. Lett. 100 140401

计量
  • 文章访问数:  8960
  • PDF下载量:  961
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-08-16
  • 修回日期:  2009-11-27
  • 刊出日期:  2010-03-05

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