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Fisher information is an important concept in estimation theory, which has recently been found closely related with the criteria of the entanglement in quantum information. Under the condition of non-rotating wave approximation, the classical phase space of the Dicke model displays chaotic dynamic properties. This paper studies the quantum Fisher information and the dynamic properties of spin squeezing in the interaction system of light and matter described in the Dicke model. Results reveal that, in the short-time instant state, wherever the initial state is, in a regular region or a chaotic region, the system displays entanglement; but in the long-time stable state, when the initial state is in the regular region, the system entanglement disappears, however, when the initial state is in the chaotic region, the system is always entangled. Compared with the spin-squeezing dynamic properties of the system, Fisher information is found to be able to effectively characterize quantum chaos. On further examination on the dynamic evolvement properties of the density matrix and purity of the system when in the regular and chaotic regions, we find that chaos gives rise to decoherence of the system, showing that quantum information become more sensitive to chaos.
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Keywords:
- quantum Fisher information /
- spin squeezing /
- quantum chaos /
- decoherence
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[2] Heller E J 1984 Phys. Rev. Lett. 53 1515
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[6] [7] Emary C, Brandes T 2003 Phys. Rev. E 67 066203
[8] Peres A 1984 Phys. Rev. A 30 1610
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[36] [37] Wang X Q, Ma J, Zhang X H, Wang X G 2009 Chin. Phys. B 20 050510
[38] Dicke R H 1954 Phys. Rev. 93 99
[39] [40] Hou X W, Chen J H, Hu B 2005 Phys. Rev. A 71 034302
[41] [42] [43] 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]
[44] Zhang W M, Feng D H, Gilmore R 1990 Rev. Mod. Phys. 62 867
[45] [46] Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press)
[47] [48] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland Press)
[49] [50] [51] Wineland D J, Bollinger J J, Itano W M, Heinzen D J 1994 Phys. Rev. A 50 67
[52] Song L J, Ma J, Yan D, Wang X G 2012 Eur. Phys. J. D 66 201
[53] [54] [55] Chaudhury S, Smith A, Anderson B E, Ghose S, Jessen P S 2009 Nature 461 768
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[1] Haake F 1991 Quantum Signature of Chaos (Berlin: Springer-Verlag press)
[2] Heller E J 1984 Phys. Rev. Lett. 53 1515
[3] [4] [5] Schack R, D'Ariano G M, Caves C M 1994 Phys. Rev. E 50 972
[6] [7] Emary C, Brandes T 2003 Phys. Rev. E 67 066203
[8] Peres A 1984 Phys. Rev. A 30 1610
[9] [10] Emerson J, Weinstein Y S, Lloyd S, Cory D G 2002 Phys. Rev. Lett. 89 284102
[11] [12] Weinstein Y S, Hellberg C S 2005 Phys. Rev. E 71 016209 Weinstein Y S, Hellberg C S 2005 Phys. Rev. E 71 035203 Weinstein Y S, Viola L 2006 Europhys. Lett. 76 746
[13] [14] [15] Furuya K, Nemes M C, Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524
[16] [17] Miller P A, Sarkar S 1999 Phys. Rev. E 60 1542
[18] Fujisaki H, Miyadera T, Tanaka A 2003 Phys. Rev. E 67 066201
[19] [20] [21] Bettelli S, Shepelyansky D L 2003 Phys. Rev. E 67 054303
[22] [23] Wang X G, Ghose S, Sanders B C, Hu B 2004 Phys. Rev. E 70 016217
[24] Novaes M, de Aguiar M A M 2004 Phys. Rev. 70 045201 Novaes M 2005 Ann. Phys. 318 308
[25] [26] [27] Song L J, Wang X G, Yan D, Zong Z G 2006 J. Phys. B: At. Mol. Opt. Phys. 39 559
[28] Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220
[29] [30] Wang X Q, Ma J, Son g L J, Zhang X H, Wang X G 2010 Phys. Rev. E 82 056205
[31] [32] Pezz L, Smerzi A 2009 Phys. Rev. Lett. 102 100401
[33] [34] [35] Zhong W, Liu J, Ma J, Wang X G 2014 Chin. Phys. B 23 060302
[36] [37] Wang X Q, Ma J, Zhang X H, Wang X G 2009 Chin. Phys. B 20 050510
[38] Dicke R H 1954 Phys. Rev. 93 99
[39] [40] Hou X W, Chen J H, Hu B 2005 Phys. Rev. A 71 034302
[41] [42] [43] 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]
[44] Zhang W M, Feng D H, Gilmore R 1990 Rev. Mod. Phys. 62 867
[45] [46] Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press)
[47] [48] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland Press)
[49] [50] [51] Wineland D J, Bollinger J J, Itano W M, Heinzen D J 1994 Phys. Rev. A 50 67
[52] Song L J, Ma J, Yan D, Wang X G 2012 Eur. Phys. J. D 66 201
[53] [54] [55] Chaudhury S, Smith A, Anderson B E, Ghose S, Jessen P S 2009 Nature 461 768
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