Dicke模型的量子经典对应关系

宋立军; 严冬; 盖永杰; 王玉波

doi:10.7498/aps.60.020302

摘要

非旋波近似条件下Dicke模型表现为量子混沌动力学特征.在详细考察Dicke模型经典相空间结构特点的基础上,采用经典-量子"一对多"的思想,即经典相空间中的一点对应于量子体系两个初始相干态的演化,利用对两个初态量子纠缠动力学演化取统计平均的方法,得到了与经典相空间对应非常好的量子相空间结构.数值计算结果表明:经典混沌有利地促进系统两体纠缠的产生,平均纠缠可以作为量子混沌的标识,利用平均纠缠可以得到一种较好的量子动力学与经典相空间的对应关系.

关键词:

Abstract

Dicke model displays quantum chaotic dynamic properties in the non-rotating wave approximation. On the basis of properties of the classical phase space of Dicke model, we employ the one-to-many notion, namely, evolution from one point on the classical phase space to two initial coherent states. Then we obtain a good quantum phase space, which corresponds to the classical one, by using the method of averaging the statistical entangled values of two initial states in the evolution. The numerical computation shows that classical chaos can promote the origination of bipartite entanglement, and simultaneously, the average entanglement can be regarded as the signature of quantum chaos. A good classica-quantum correspondence can be obtained by using the average entanglement.

Keywords:

作者及机构信息

(1)长春大学理学院,长春 130022; (2)长春理工大学理学院,长春 130022

基金项目: 国家自然科学基金(批准号:10947019)、吉林省自然科学基金(批准号:20101514)和吉林省教育厅科技研究基金(批准号:2009237)资助的课题.

Authors and contacts

(1)School of Science, Changchun University of Science and Technology, Changchun 130022, China; (2)School of Science, Changchun University, Changchun 130022, China

参考文献

[1]	Ott E 2002 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)
[2]	Haake F 1991 Quantum Signature of Chaos (Berlin:Springer-Verlag)
[3]	Furuya K, Nemes M C, Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524
[4]	Wang X G, Ghose S, Sanders B C, Hu B 2004 Phys. Rev.E 70 016217
[5]	Hou X W, Chen J H, Hu B 2004 Phys. Rev. A 69 042110
[6]	Hou X W, Chen J H, Hu B 2005 Phys. Rev. A 71 034302
[7]	Emerson J, Weinstein Y S, Lloyd S, Cory D G 2002 Phys. Rev. Lett. 89 284102
[8]	Weinstein Y S, Hellberg C S 2005 Phys. Rev. E 71 016209
[9]	Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 0661 (in Chinese) [房永翠、杨志安、杨丽云 2008 57 0661]
[10]	Ouyang X C, Fang M F, Kang G D, Deng X J, Huang L Y 2010 Chin. Phys. B 19 030309
[11]	Zhang Y J, Xia Y J, Ren Y Q, Du X M, Liu Y L 2009 Acta Phys. Sin. 58 0722 (in Chinese) [张英杰、夏云杰、任延琦、杜秀梅、刘玉玲 2009 58 0722]
[12]	Guo L, Liang X T 2009 Acta Phys. Sin. 58 0050 (in Chinese) [郭亮、梁先庭 2009 58 0050]
[13]	Lu P, Wang S J 2009 Acta Phys. Sin. 58 5955 (in Chinese) [卢鹏、王顺金 2009 58 5955]
[14]	Meng S Y, Wu W 2009 Acta Phys. Sin. 58 5311 (in Chinese) [孟少英、吴炜 2009 58 5311]
[15]	Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623
[16]	Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2006 Phys. Lett. A 353 216
[17]	Gorin T, Prosen T, Seligman T H, Znidaric M 2006 Phys. Rep. 435 33
[18]	Song L J, Wang X G, Yan D, Zong Z G 2006 J. Phys. B: At. Mol. Opt. Phys. 39 559
[19]	Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220
[20]	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 58 3679]
[21]	Chaudhury S, Smith A, Anderson B E, Ghose S, Jessen P S 2009 Nature 461 768
[22]	Dicke R H 1954 Phys. Rev. 93 99
[23]	Zhang W M, Feng D H, Gilmore R 1990 Rev. Mod. Phys. 62 867

施引文献

[1]	Ott E 2002 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)
[2]	Haake F 1991 Quantum Signature of Chaos (Berlin:Springer-Verlag)
[3]	Furuya K, Nemes M C, Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524
[4]	Wang X G, Ghose S, Sanders B C, Hu B 2004 Phys. Rev.E 70 016217
[5]	Hou X W, Chen J H, Hu B 2004 Phys. Rev. A 69 042110
[6]	Hou X W, Chen J H, Hu B 2005 Phys. Rev. A 71 034302
[7]	Emerson J, Weinstein Y S, Lloyd S, Cory D G 2002 Phys. Rev. Lett. 89 284102
[8]	Weinstein Y S, Hellberg C S 2005 Phys. Rev. E 71 016209
[9]	Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 0661 (in Chinese) [房永翠、杨志安、杨丽云 2008 57 0661]
[10]	Ouyang X C, Fang M F, Kang G D, Deng X J, Huang L Y 2010 Chin. Phys. B 19 030309
[11]	Zhang Y J, Xia Y J, Ren Y Q, Du X M, Liu Y L 2009 Acta Phys. Sin. 58 0722 (in Chinese) [张英杰、夏云杰、任延琦、杜秀梅、刘玉玲 2009 58 0722]
[12]	Guo L, Liang X T 2009 Acta Phys. Sin. 58 0050 (in Chinese) [郭亮、梁先庭 2009 58 0050]
[13]	Lu P, Wang S J 2009 Acta Phys. Sin. 58 5955 (in Chinese) [卢鹏、王顺金 2009 58 5955]
[14]	Meng S Y, Wu W 2009 Acta Phys. Sin. 58 5311 (in Chinese) [孟少英、吴炜 2009 58 5311]
[15]	Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623
[16]	Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2006 Phys. Lett. A 353 216
[17]	Gorin T, Prosen T, Seligman T H, Znidaric M 2006 Phys. Rep. 435 33
[18]	Song L J, Wang X G, Yan D, Zong Z G 2006 J. Phys. B: At. Mol. Opt. Phys. 39 559
[19]	Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220
[20]	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 58 3679]
[21]	Chaudhury S, Smith A, Anderson B E, Ghose S, Jessen P S 2009 Nature 461 768
[22]	Dicke R H 1954 Phys. Rev. 93 99
[23]	Zhang W M, Feng D H, Gilmore R 1990 Rev. Mod. Phys. 62 867

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