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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.
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Keywords:
- Dicke model /
- non rotating wave approximation /
- quantum chaos /
- classical-quantum correspondence
[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 物理学报 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 物理学报 58 0722]
[12] Guo L, Liang X T 2009 Acta Phys. Sin. 58 0050 (in Chinese) [郭 亮、梁先庭 2009 物理学报 58 0050]
[13] 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]
[14] Meng S Y, Wu W 2009 Acta Phys. Sin. 58 5311 (in Chinese) [孟少英、吴 炜 2009 物理学报 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 物理学报 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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[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 物理学报 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 物理学报 58 0722]
[12] Guo L, Liang X T 2009 Acta Phys. Sin. 58 0050 (in Chinese) [郭 亮、梁先庭 2009 物理学报 58 0050]
[13] 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]
[14] Meng S Y, Wu W 2009 Acta Phys. Sin. 58 5311 (in Chinese) [孟少英、吴 炜 2009 物理学报 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 物理学报 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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