光与物质相互作用系统中的量子Fisher信息和自旋压缩

常锋; 王晓茜; 盖永杰; 严冬; 宋立军

doi:10.7498/aps.63.170302

摘要

Fisher信息是估计理论中的重要概念，最近发现与量子信息中的纠缠判据具有密切联系. 非旋波近似条件下，Dicke模型经典相空间表现为混沌动力学特征.本文详细考察了Dicke 模型描述的光与物质相互作用系统中量子Fisher信息和自旋压缩动力学特性. 结果表明：在短时瞬态情况下，无论初态处于规则区域还是混沌区域系统均表现为纠缠性质；但在长时稳态情况下，初态处于规则区域时系统纠缠消失，而初态处于混沌区域时系统则一直存在纠缠. 通过与系统自旋压缩动力学性质相比较，发现量子Fisher信息可以更有效地刻画量子混沌. 进一步考察初态处于规则和混沌区域时系统密度矩阵和纯度的动力学演化特性，发现混沌导致系统退相干现象发生，说明量子Fisher信息对混沌更敏感.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
长春理工大学理学院, 长春 130022;

2.
长春大学理学院, 长春 130022

基金项目: 国家自然科学基金（批准号：11347013，11305020）、吉林省科技发展计划项目（批准号：20130521016JH，20140101187JC）和吉林省教育厅科技发展计划项目（批准号：2012245，2013262）资助的课题.

Authors and contacts

1.
Department of Physics, Changchun University of Science and Technology, Changchun 130022, China;

2.
Department of Physics, Changchun University, Changchun 130022, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11347013, 11305020), and the Science Foundation of Jilin Province, China (Grant Nos. 20130521016JH, 20140101187JC), the Scientific Foundation of the Education Department of Jilin Province, China (Grant Nos. 2012245, 2013262).

参考文献

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施引文献

[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 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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