非马尔科夫环境下量子系统的非经典效应
|
摘要
量子系统间的相互作用导致许多不同于经典物理的奇特量子效应——非经典效应。一般情况下,真实的量子系统是开放系统,它会与外部环境发生相互作用,从而导致其非经典效应的损伤甚至消失。如何选择合适的环境,通过量子调控技术保持或增强量子系统的非经典效应,是量子光学研究领域人们关心的热点问题。近年来人们注意到具有记忆效应的非马尔科夫环境对量子系统的动力学行为具有回复作用。那么,在非马尔科夫环境下,是否能通过量子调控技术实现量子系统的非经典效应的保持或增强?本文运用开放量子系统的基本理论研究了非马尔科夫环境下量子系统的非经典效应,取得了一些有创新意义的结果。主要内容如下：
第一章简单介绍了非马尔科夫开放量子系统的基本理论和几种典型的量子非经典效应。
第二章用时间消卷积主方程方法研究了与两个独立库失谐耦合的二能级原子系统的熵不确定度与纠缠见证。详细讨论了在量子存储支撑下,非马尔科夫效应和失谐量对熵不确定关系和纠缠见证的影响。结果表明：只有在全同的非马尔科夫库中,增大失谐和非马尔科夫效应才能减小测量输出的熵不确定度、减小熵不确定关系下限、增加纠缠见证时间、有效保持纠缠见证区域。这些结果在量子测量、量子密码和量子信息处理中具有实际应用价值。
第三章基于第二章的模型,研究了两原子的压缩效应,发现两原子压缩同时依赖于失谐和非马尔科夫效应。结果表明：在非马尔科夫环境下,失谐越大、非马尔科夫效应越强,压缩效应保护得越好,而且当失谐和非马尔科夫效应同时存在时,两原子压缩能有效地长时间保持。该结果在自旋偏振测量、高精度原子钟制造等方面具有实际意义。
第四章利用时间消卷积主方程方法研究了非马尔科夫环境中两原子-腔系统的纠缠动力学,首次得到了非马尔科夫环境下两原子-腔系统的精确解析解,并详细讨论了原子-腔耦合强度、非马尔科夫效应和初态纯度对纠缠动力学的影响。结果表明：两原子之间的纠缠与两腔模之间的纠缠可以相互交换,在短时间内,几对纠缠相互交换并振荡地衰减,当时间足够长时,四对纠缠会呈现单调减小的规律；获得了两原子-腔系统中任意两量子比特的纠缠稳态；提出了在原子-腔耗散系统中利用原子和腔之间的相互作用实现纠缠交换的方案；提供了在非马尔科夫环境中利用原子-腔之间的相互作用实现由一对纠缠态制备多对纠缠态的纠缠复制新方法。该结果在量子信息、量子通信、量子计算等许多领域中都起着极其重要的作用。
第五章利用时间消卷积主方程方法,分别针对洛伦兹谱密度和具有Lorentz-Drude截断频率的欧米伽谱密度的环境,研究了两原子之间的量子谐错,讨论了非马尔科夫环境的性质对量子谐错的影响。结果表明：在不同性质的非马尔科夫环境中,量子谐错都能得到很好的保持,而且非马尔科夫效应越强、失谐量越大,量子谐错的鲁棒性越好。
第六章基于第五章的模型,研究了不同非马尔科夫环境中两原子激发态的布居囚禁,讨论了非马尔科夫环境的性质对原子布居囚禁的影响。结果表明：在不同性质的非马尔科夫库中,两原子激发态布居都能得到很好的囚禁,而且非马尔科夫效应越强、失谐量越大,两原子激发态布居的囚禁效果越好。
第七章对全文进行了总结与展望。
Non-classical effects of quantum system are peculiar quantum effects different from the classical physics, which are caused by interactions between quantum sys-tems. Generally, interactions with outside environments will destroy non-classical effects of open quantum systems. It has become a hot issue in the quantum optics field how to maintain or enhance non-classical effects of open quantum systems by quantum controlling technology. In recent years, it has been noted that the mem-ory effects of non-Markovian environments can make the dynamical behaviors of quantum systems recovered. Whether can the non-classical effects be maintained or enhanced by quantum controlling technology in non-Markovian environments? The aim of this paper is to investigate the non-classical effects of two independent two-level atoms in non-Markovian environments. The main contents are as follows:
1.Several typical non-classical effects of quantum system and the basic theory of open quantum system are introducted briefly.
2.The quantum entropic uncertainty and entanglement witness in two-atom system coupling with non-Markovian environments is studied by the time-convolutionless master-equation approach. The influence of non-Markovian effect and detuning on the quantum entropic uncertainty relation and entanglement witness in the presence of quantum memory is discussed in detail. The result shows that, only when two non-Markovian reservoirs are identical, the increasing detuning and non-Markovian effect can cut down the entropic uncertainty of measurement outcomes, reduce the lower bound of the entropic uncertainty relation, increase the time re-gion during which the entanglement can be witnessed, and effectively protect the entanglement region witnessed by the lower bound of the entropic uncertainty rela-tion. The results can be applied in quantum measurement, quantum cryptography task and quantum information processing.
3.The squeezing dynamics of two atoms is researched, based on the model of Chapter2. The results show that, in the non-Markovian regime, the bigger the detuning and the stronger the non-Markovian effect are, the better the squeezing is preserved. And the squeezing of two atoms can be effectively protected for a long time when both non-Markovian effect and detuning are present simultane-ously. The results would be useful in high-precision measurement and quantum communication.
4.Analytical solution and entanglement swapping of two atom-cavity system, where each cavity is coupled to a Lorentzian reservoir, has been investigated by the non-Markovian master equation method. We first gain the analytical solution of two atom-cavity system in non-Markovian environments and discuss in detail the influence of the atom-cavity coupling, the non-Markovian effect and the initial state purity on the entanglement dynamics and the entanglement swapping. The results show that, the entanglement can be swapped between any two qubits by the interaction, such as between two atoms, between two cavities and between a atom and its cavity. In a short time, several pairs of entanglement alternate and decrease oscillate damply, but after a long time, four pairs of entanglement will decrease monotonically. We obtain two steady entanglement states in Marko-vian and non-Markovian regimes, respectively, and put forward an entanglement swapping scheme utilizing interaction atom with cavity in two atom-cavity dissi-pative system, and provide a new way copying entanglement that several pairs of entanglement can be simultaneously prepared by a pair of entanglement in non-Markov environments. The results will play a crucial role in quantum information, quantum communication and quantum computing.
5.The quantum discord of two atoms, which are in two Ohmic reservoirs or in two Ohmic reservoirs with a Lorentz-Drude cutoff function, respectively, is considered. We find that, the quantum discord can be effectively protected not only in Lorentzian reservoirs but also in Ohmic reservoirs with a Lorentz-Drude cutoff function, and the bigger the detuning and the stronger the non-Markovian effect are, the better the robustness of the quantum discord is.
6.The population dynamics of two atoms is discussed by means of the idea of Chapter5. The results show that the two atoms can be effectively trapped in the excited states not only in Lorentzian reservoirs but also in Ohmic reservoirs with a Lorentz-Drude cutoff function.
7.A summary and outlook is presented.
第一章简单介绍了非马尔科夫开放量子系统的基本理论和几种典型的量子非经典效应。
第二章用时间消卷积主方程方法研究了与两个独立库失谐耦合的二能级原子系统的熵不确定度与纠缠见证。详细讨论了在量子存储支撑下,非马尔科夫效应和失谐量对熵不确定关系和纠缠见证的影响。结果表明：只有在全同的非马尔科夫库中,增大失谐和非马尔科夫效应才能减小测量输出的熵不确定度、减小熵不确定关系下限、增加纠缠见证时间、有效保持纠缠见证区域。这些结果在量子测量、量子密码和量子信息处理中具有实际应用价值。
第三章基于第二章的模型,研究了两原子的压缩效应,发现两原子压缩同时依赖于失谐和非马尔科夫效应。结果表明：在非马尔科夫环境下,失谐越大、非马尔科夫效应越强,压缩效应保护得越好,而且当失谐和非马尔科夫效应同时存在时,两原子压缩能有效地长时间保持。该结果在自旋偏振测量、高精度原子钟制造等方面具有实际意义。
第四章利用时间消卷积主方程方法研究了非马尔科夫环境中两原子-腔系统的纠缠动力学,首次得到了非马尔科夫环境下两原子-腔系统的精确解析解,并详细讨论了原子-腔耦合强度、非马尔科夫效应和初态纯度对纠缠动力学的影响。结果表明：两原子之间的纠缠与两腔模之间的纠缠可以相互交换,在短时间内,几对纠缠相互交换并振荡地衰减,当时间足够长时,四对纠缠会呈现单调减小的规律；获得了两原子-腔系统中任意两量子比特的纠缠稳态；提出了在原子-腔耗散系统中利用原子和腔之间的相互作用实现纠缠交换的方案；提供了在非马尔科夫环境中利用原子-腔之间的相互作用实现由一对纠缠态制备多对纠缠态的纠缠复制新方法。该结果在量子信息、量子通信、量子计算等许多领域中都起着极其重要的作用。
第五章利用时间消卷积主方程方法,分别针对洛伦兹谱密度和具有Lorentz-Drude截断频率的欧米伽谱密度的环境,研究了两原子之间的量子谐错,讨论了非马尔科夫环境的性质对量子谐错的影响。结果表明：在不同性质的非马尔科夫环境中,量子谐错都能得到很好的保持,而且非马尔科夫效应越强、失谐量越大,量子谐错的鲁棒性越好。
第六章基于第五章的模型,研究了不同非马尔科夫环境中两原子激发态的布居囚禁,讨论了非马尔科夫环境的性质对原子布居囚禁的影响。结果表明：在不同性质的非马尔科夫库中,两原子激发态布居都能得到很好的囚禁,而且非马尔科夫效应越强、失谐量越大,两原子激发态布居的囚禁效果越好。
第七章对全文进行了总结与展望。
Non-classical effects of quantum system are peculiar quantum effects different from the classical physics, which are caused by interactions between quantum sys-tems. Generally, interactions with outside environments will destroy non-classical effects of open quantum systems. It has become a hot issue in the quantum optics field how to maintain or enhance non-classical effects of open quantum systems by quantum controlling technology. In recent years, it has been noted that the mem-ory effects of non-Markovian environments can make the dynamical behaviors of quantum systems recovered. Whether can the non-classical effects be maintained or enhanced by quantum controlling technology in non-Markovian environments? The aim of this paper is to investigate the non-classical effects of two independent two-level atoms in non-Markovian environments. The main contents are as follows:
1.Several typical non-classical effects of quantum system and the basic theory of open quantum system are introducted briefly.
2.The quantum entropic uncertainty and entanglement witness in two-atom system coupling with non-Markovian environments is studied by the time-convolutionless master-equation approach. The influence of non-Markovian effect and detuning on the quantum entropic uncertainty relation and entanglement witness in the presence of quantum memory is discussed in detail. The result shows that, only when two non-Markovian reservoirs are identical, the increasing detuning and non-Markovian effect can cut down the entropic uncertainty of measurement outcomes, reduce the lower bound of the entropic uncertainty relation, increase the time re-gion during which the entanglement can be witnessed, and effectively protect the entanglement region witnessed by the lower bound of the entropic uncertainty rela-tion. The results can be applied in quantum measurement, quantum cryptography task and quantum information processing.
3.The squeezing dynamics of two atoms is researched, based on the model of Chapter2. The results show that, in the non-Markovian regime, the bigger the detuning and the stronger the non-Markovian effect are, the better the squeezing is preserved. And the squeezing of two atoms can be effectively protected for a long time when both non-Markovian effect and detuning are present simultane-ously. The results would be useful in high-precision measurement and quantum communication.
4.Analytical solution and entanglement swapping of two atom-cavity system, where each cavity is coupled to a Lorentzian reservoir, has been investigated by the non-Markovian master equation method. We first gain the analytical solution of two atom-cavity system in non-Markovian environments and discuss in detail the influence of the atom-cavity coupling, the non-Markovian effect and the initial state purity on the entanglement dynamics and the entanglement swapping. The results show that, the entanglement can be swapped between any two qubits by the interaction, such as between two atoms, between two cavities and between a atom and its cavity. In a short time, several pairs of entanglement alternate and decrease oscillate damply, but after a long time, four pairs of entanglement will decrease monotonically. We obtain two steady entanglement states in Marko-vian and non-Markovian regimes, respectively, and put forward an entanglement swapping scheme utilizing interaction atom with cavity in two atom-cavity dissi-pative system, and provide a new way copying entanglement that several pairs of entanglement can be simultaneously prepared by a pair of entanglement in non-Markov environments. The results will play a crucial role in quantum information, quantum communication and quantum computing.
5.The quantum discord of two atoms, which are in two Ohmic reservoirs or in two Ohmic reservoirs with a Lorentz-Drude cutoff function, respectively, is considered. We find that, the quantum discord can be effectively protected not only in Lorentzian reservoirs but also in Ohmic reservoirs with a Lorentz-Drude cutoff function, and the bigger the detuning and the stronger the non-Markovian effect are, the better the robustness of the quantum discord is.
6.The population dynamics of two atoms is discussed by means of the idea of Chapter5. The results show that the two atoms can be effectively trapped in the excited states not only in Lorentzian reservoirs but also in Ohmic reservoirs with a Lorentz-Drude cutoff function.
7.A summary and outlook is presented.
引文
[1]M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Informa-tion[M]. Cambridge:Cambridge University Press,2000.
[2]C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters. Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels[J]. Phys. Rev. Lett.1993,70:1895.
[3]D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger, Experimental Quantum Teleportation[J]. Nature,1997,390:575.
[4]M. Keyl, Fundamentals of Quantum Information Theory[J]. Phys. Rep.2002, 369:431.
[5]G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rotteler, H. Weinfurter, R. Werner and A. Zeilinger, Quantum Information:An Introduction to Basic Theoretical Concepts and Experiments[J]. Beijing:World Publishing Cor-poratin,2004.
[6]V. Vedral, Introdution to Quantum Information Science[M]. Oxford:Oxford Uni-versity Press,2006.
[7]L. Amico, R. Fazio, A. Osterloh and V. Vedral, Entanglement in Many-Body Systems[J]. Rev. Mod. Phys.2008,80:517.
[8]H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems[M]. Ox-ford:Oxford University Press,2007.
[9]C. W. Gardiner and P. Zoller,Quantum Noise[M]. Berlin:Springer-Verlag Press, 1999.
[10]U. Weiss, Quantum Dissipative Systems[M]. Singapore:World Scientific Press, 2008.
[11]B. J. Dalton, S. M. Barnett and B. M. Garraway, Theory of Pseudom.odes in Quantum Optical Processes [J]. Phys. Rev. A 2001,64:053813.
[12]A. Wallraff, et.al., Strong coupling of a single photon to a superconducting qubit using circuit quantumelectrodynamics[J]. Nature 2004,431:162.
[13]J. P. Reithmaier et al., Strong coupling in a single quantum dot-semiconductor microcavity system[J]. Nature 2004,432:197.
[14]P. Lambropoulos et al., Fundamental quantum optics in structured reservoirs[J]. Rep. Prog. Phys.2000,63:455.
[15]C. W. Lai, P. Maletinsky, A. Badolato and A. Imamoglu, Knight-Field-Enabled Nuclear Spin Polarization in Single Quantum Dots[J]. Phys. Rev. Lett.2006, 96:167403.
[16]A. Pomyalov and D. J. Tannor, The non-Markovian quantum master equation in the collective-mode representation:Application to barrier crossing in the interme-diate friction regime[J]. J. Chem. Phys.2005,123:204111.
[17]Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger and J. Reichel, Strong Atom-Field Coupling for Bose-Einstein Condensates in an Optical Cavity on a Chip[J]. Nature 2007,450:272.
[18]K. Hennessy, et. al., Quantum nature of a strongly coupled single quantum dot-cavity system[J]. Nature 2007,445:896.
[19]W. Heisenberg, Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[J]. Z. Phys.1927,43:172.
[20]I. Bialynicki-Birula, Entropic uncertainty relations[J]. Phys. Lett. A 1984,103: 253.
[21]I. Bialynicki-Birula and J. L. Madajczyk, Entropic uncertainty relations for angu-lar distributions[J]. Phys. Lett. A 1985,108:384.
[22]J. A. Vaccaro and R. F. Bonner, Pegg-Barnett phase operators of infinite rank[J]. Phys. Lett. A 1995,198:167.
[23]I. I. Hirschman, A note on entropy[J]. Amer. J. Math.1957,79:152.
[24]D. Deutsch, Uncertainty in Quantum Measurements[J]. Phys. Rev. Lett.1983, 50:631.
[25]K. Kraus, Complementary observables and uncertainty relations[J]. Phys. Rev. D 1987,35:3070.
[26]H. Maassen and J. B. Uffink, Generalized entropic uncertainty relations[J]. Phys. Rev. Lett.1988,60:1103.
[27]J. Sanchez-Ruiz, Entropic uncertainty and certainty relations for complementary observables[J]. Phys. Lett. A 1993,173:233.
[28]J. M. Renes and J.-C. Boilean, Conjectured Strong Complementary Information Tradeoff[J]. Phys. Rev. Lett.2009,103:020402.
[29]M. Berta,M.Christandl, R. Colbeck, J. M. Renes and B.Benner, The Uncertainty Principle in the Presence of Quantum Memory[J]. Nat. Phys.2010,6:659.
[30]R. Prevedel, D. R. Hamel, R. Colbeck, K. Fisher and K. J. Resch, Experimental investigation of the uncertainty principle in the presence of quantum memory[J]. Nat. Phys.2011,7:757.
[31]C. F. Li, J. S. Xu, X. Y. Xu, K. Li and G. C. Guo, Experimental investigation of the entanglement-assisted entropic uncertainty principle[J]. Nat. Phys.2011,7: 752.
[32]M. Tomamichel, C. C. W. Lim, N. Gisin and R. Renner, Tight Finite-Key Analysis for Quantum Cryptography[J]. Nature Commun.2012,3:634.
[33]D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin and B. M. Terhal, Locking classical correlations in quantum states[J]. Phys. Rev. Lett.2004,92: 067902.
[34]P. Nataf, M. Dogan and K. L. Hur, Heisenberg uncertainty principle as a probe of entanglement entropy:Application to superradiant quantum phase transitions[J]. Phys. Rev. A 2012,86:043807.
[35]M.-L. Hu and H. Fan, Quantum-memory-assisted, entropic uncertainty principle. teleportation. and entanglement witness in structured reservoirs[J]. Phys. Rev. A 2012,86:032338.
[36]G. M. Gaves, Quantum-mechanical noise in an interferometer[J]. Phys. Rev. D 1981,23:1693.
[37]R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Quantum Eentan-glement[J]. Rev. Mod. Phys.2009,81:865.
[38]O. Guehne and G. Toth, Entanglement detection[J]. Phys. Rep.2009,474:1.
[39]S. L. Braunstein and P. van Loock, Quantum information with continuous vari-ables[J]. Rev. Mod. Phys.2005,77:513.
[40]I. D. Leroux, M. H. Schleier-Smith and V. Vuletic, Implementation of Cavity Squeezing of a Collective Atomic Spin[J]. Phys. Rev. Lett.2010,104:073602.
[41]D. J. Wineland, J. J. Bollonger and W. M. Itano, Squeezed atomic states and projection noise in spectroscopy[J]. Phys. Rev. A 1994,50:67.
[42]K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari,K. Mckenzie, R. Ward, S. Vass, A. J. Weinstein and N. Mavalvala, A quantum-enhanced prototype gravitational-wave detector[J].Nat. Phys.2008,4:472.
[43]J. A. Dunningham and K. Burnett, Sub-shot-noise-limited measurements with Bose-Einstein condensates[J]. Phys. Rev. A 2004,70:033601.
[44]M. Kitagawa and M. Ueda, Squeezed spin states[J]. Phys. Rev. A 1993,47: 5138.
[45]J.-Ma, X.-G. Wang, C. P. Sun and Franco Nori, Quantum spin squeezing[J]. Phys. Rep.2011,509:89.
[46]X. Wang and B. C. Sanders, Spin squeezing and pairwise entanglement for sym-metric multiqubit states[J]. Phys. Rev. A 2003,68:012101.
[47]A. S(?)rensen and K. M(?)lmer, Spin-Spin Interaction and Spin Squeezing in an Op-tical Lattice[J]. Phys. Rev. Lett.1999,83:2274.
[48]G. Toth, C. Knapp,O. Giihne, and H. J. Briegel, Optimal Spin Squeezing Inequal-ities Detect Bound Entanglement in Spin Models[J]. Phys. Rev. Lett.2007,99: 250405.
[49]G. T6th,C. Knapp, O. Giihne, and H. J. Briegel, Spin squeezing and entanglemen-t[J]. Phys. Rev. A 2009,79:042334.
[50]E. Knill and R. Laflamme, Power of One Bit of Quantum Information[J]. Phys. Rev. Lett.1998,81:5672.
[51]N. Gisin and R. Thew, Quantum Communication[J]. Nat. Photonics 2007,1: 165.
[52]S. Lloyd, Universal Quantum Simulators[J]. Science 1996,273:1073.
[53]M. F. Santos, P. Milman, L. Davidovich and N. Zagury, Direct measurement of finite-time disentanglement induced by a reservoir[J]. Phys. Rev. A 2006,73: 040305(R).
[54]T. Yu and J. H. Eberly, Finite-Time Disentanglement Via Spontaneous Emis-sion[J]. Phys. Rev. Lett.2004,93:140404.
[55]T. Yu and J.H. Eberly, Sudden death of entanglement[J]. Science 2009,323:598.
[56]M. P. Almeida et al., Experimental Observation OF Finite-Time Disentanglemen-t[J]. Science 2007,316:579.
[57]B. Bellomo, R. Lo Franco and G. Compagno, Non-Markovian Effects on the Dy-namics of Entanglement[J]. Phys. Rev. Lett.2007,99:160502.
[58]B. Bellomo, R. Lo Franco and G. Compagno, Entanglement dynamics of two independent qubits in environments with and without memory [J]. Phys. Rev. A 2008,77:032342.
[59]B. Bellomo, R. Lo Franco, S. Maniscalco and G. Compagno, Entanglement Trap-ping in Structured Environments[J]. Phys. Rev. A 2008,78:060302(R).
[60]M. Ban, S. Kitajima and F. Shibata, Decoherence of quantum information in the non-Markovian qubit channel[J]. J. Phys. A:Math. Gen.2005,38:7161.
[61]E. Bihama,G. Brassardb, D. Kenigsberga and T. Mor, Quantum, Computing With-out Entanglement[J]. Theor. Comput. Sci.2004,320:15.
[62]L. Henderson and V. Vedral, Classical. Quantum and Total Correlations[J]. J. Phys. A:Math. Theor.2001,34:6899.
[63]H. Ollivier and W. H. Zurek, Quantum discord:A Measure of the Quantumness of Correlations[J]. Phys. Rev. Lett.2001,88:017901.
[64]B. P. Lanyon, M. Barbieri, M. P. Almeida and A. G. White, Experimental Quan-tum Computing without, Entanglement[J]. Phys. Rev. Lett.2008,101:200501.
[65]P. Giorda and M. G. A. Paris, Gaussian Quantum discord [J]. Phys. Rev. Lett. 2010,105:020503.
[66]D. Cavalcanti, L. Aolita, S. Boixo, K. Modi, M. Piani and A. Winter, Operational Interpretations of Quantum. discord[J]. Phys. Rev. A 2011,83:032324.
[67]S. Luo and S. Fu, Geometric Measure of Quantum discord[J]. Phys. Rev. A 2010, 82:034302.
[68]S. Luo, Quantum discord for Two-Qubit Systems[J]. Phys. Rev. A 2008,77: 042303.
[69]C. C. Rulli and M. S. Sarandy, Global Quantum discord in Multipartite Systems[J]. Phys. Rev. A 2011,84:042109.
[70]L. Ciliberti, R. Rossignoli, and N. Canosa, Quantum discord in Finite XY Chain-s[J]. Phys. Rev. A 2010,82:042316.
[71]B. Li, Z. X. Wang and S. M. Fei, Quantum discord and Geometry for a Class of Two-Qubit States[J]. Phys. Rev. A 2010,83:022321.
[72]C K. Lee, L. C. Kwek and J. Cao, Stochastic Resonance of Quantum discord[J]. Phys. Rev. A 2011,84:062113.
[73]C. Zhang, S. Yu, Q. Chen and C. H. Oh, Detecting the Quantum discord of an Unknown State by a Single Observable[J]. Phys. Rev. A 2011,84:032122.
[74]A. Streltsov, H. Kampermann, and D. Brufβ, Behavior of Quantum Correlations under Local Noise[J]. Phys. Rev. Lett.2011,107:170502.
[75]H. I. Yoo and J. H. Eberly, Dynamical theory of an atom with two or three levels interacting with quantized cavity fields Review Article[J]. Phys. Rep.1985,118: 239.
[76]P. M. Radmore, Population trapping in a multilevel system[J]. Phys. Rev. A 1982,26:2252.
[77]Z. Deng and J. H. Eberly, Coherent trapping in continuum-continuum transition-s[J]. Phys. Rev. A 1986,34:2492.
[78]J. I. Cirac and L. L. Sanchez-Soto, Population trapping in the Jaynes-Cummings model via phase coupling[J]. Phys. Rev. A 1990,42:2851.
[79]J. I. Cirac and L.L. Sanchez-Soto, Population trapping in two-level models:Spectral and statistical properties[J]. Phys. Rev. A 1991,44:3317.
[80]G. S. Agarwal, Coherent population trapping states of a system interacting with quantized fields and the production of the photon statistics matched fields[J]. Phys. Rev. Lett.1993,71:1351.
[81]W. D. Phillips, Laser cooling and trapping of neutral atoms[J]. Rev. Mod. Phys. 1998,70:721.
[82]K. Bergmann, H. Theuer and B. W. Shore, Coherent population transfer among quantum states of atoms and molecules[J]. Rev. Mod. Phys.1998,70:1003.
[83]P. Kral, I. Thanopulos and M. Shapiro, Colloquium:Coherently controlled adia-batic passage[J]. Rev. Mod. Phys.2007,79:53.
[84]M. Fleischhauer, A. Imamoglu and J. P. Marangos, Electromagnetically induced transparency:Optics in coherent media [J]. Rev. Mod. Phys.2005,77:633.
[85]M. D. Lukin, Colloquium:Trapping and manipulating photon states in atomic ensembles[J]. Rev. Mod. Phys.2003,75:457.
[86]J. Mompart and R. Corbalan, Lasing without inversion[J]. J. Opt. B:Quantum Semiclass. Opt.2000,2:R7.
[87]B. Lev et al, Feasibility of detecting single atoms using photonic bandgap cavi-ties[J]. Nanotechnology 2004,15:S556.
[88]L. Florescu, S. John, T. Quang and R. Wang, Theory of a one-atom laser in a photonic band-gap microchip[J]. Phys. Rev. A 2004,69:013816.
[89]肖兴,开放量子系统的非马尔科夫动力学和弱测量反馈控制[D].湖南：湖南师范大学博士学位论文,2012.
[90]W. H. Zurek, Decoherence, Einselection. and the Quantum Origins of the Classi-cal[J]. Rev. Mod. Phys.2003,75:715.
[91]曾谨言,量子力学[M].北京：科学出版社,2001.
[92]K. Hornberger, Introduction to Decoherence Theory[J]. Lect. Notes Phys.2009, 768:221.
[93]G. Landblad, On the Generators of Quantum Dynamical Semigroups[J]. Com-mun. Math. Phys.1976,48:119.
[94]W. H. Louisell, Quantum Statistical Properties of Radiation[M]. New York:Wiley, 1973.
[95]S. Nakajima, On Quantum Theory of Transport Phenomena[J]. Prog. Theor. Phys.1958,20:948.
[96]R. Zwanzig, Ensemble Method in the Theory of Irreversibility[J]. J. Chem. Phys. 1960,33:1338.
[97]S. Chaturvedi and F. Shibata, Time-Convolutionless Projection Operator Formal-ism for Elimination of Fast Variables:Applications to Brownian Motion[J]. Z. Phys. B 1979,35:297.
[98]H.-P. Breuer, B. Kapplera and F. Petruccionea, The Time-Convolutionless Pro-jection Operator Technique in the Quantum Theory of Dissipation and Decoher-ence[J]. Ann. Phys.2002,291:36.
[99]A. Shabani and D. A. Lidar, Completely Positive Post-Markovian Master Equation via a Measurement Approach[J]. Phys. Rev. A 2005,71:020101(R).
[100]G. Schaller and T. Brandes, Preservation of Positivity by Dynamical Coarse Grain-ing[J]. Phys. Rev. A 2008,78:022106.
[101]M. M. Jack, Non-Markovian Quantum Trajectories[D]. University of Auckland, PhD Thesis,1999.
[102]I. Bialynicki-birula and J. Mycielski, Uncertainty relations for information entropy in wave mechanics[J]. Commun. Math. Phys.1975,44:129.
[103]Y.-K. Kim and Y. Shih, Experimental realization of Popper's Experiment:Viola-tion of the Uncertainty Principle[J]. Found. Phys.1999,29:1849.
[104]H. F. Hofmann and S. Takeuchi, Violation of local uncertainty relations as a sig-nature of entanglement[J]. Phys. Rev. A 2003,68:032103.
[105]I. Devetak and A. Winter, Distillation of secret key and entanglement from quan-tum states[J]. Proc. R. Soc. A 2005,461:207.
[106]彭金生,李高翔,近代量子光学导论[M].北京：科学出版社,1996.
[107]D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy[J]. Phys. Rev. A 1992,46: R6797.
[108]X. Xiao, M. F. Fang and Y. M. Hu, Protecting Atomic Squeezing by Detuning in Non-Markovian Environments[J]. Phys. Scr.2011,84:045011.
[109]L. Henderson and V. Vedral, Information, Relative Entropy of Entanglement, and Irreversibility[J]. Phys. Rev. Lett.2000,84:2263.
[110]S. Bose and V. Vedral, Mixedness and teleportation[J]. Phys. Rev. A.2000,61: 040101(R).
[111]P. Horodecki, Separability criterion and inseparable mixed states with positivepar-tial transposition[J]. Phys. Lett. A 1997,232:333.
[112]W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubit-s[J]. Phys. Rev. Lett.1998,80:2245.
[113]K. Modi, T. Paterek, W. Son, V. Vedral and M. Williamson, Unified View of Quantum and Classical Correlations[J]. Phys. Rev. Lett.2010,104:080501.
[114]B. Dakic, V. Vedral and C. Brukner, Necessary and Sufficient Condition for Nonzero Quantum discord[J]. Phys. Rev. Lett.2010,105:190502.
[115]Z.-Y. Xu, W. L. Yang and M. Feng, Quantum-memory-assisted entropic uncer-tainty relation under noise[J]. Phys. Rev. A 2012,86:012113.
[116]A. K. Pati, M. M. Wilde, A. R. Usha Devi, A. K. Rajagopal and Sudha, Quan-tum discord and classical correlation can tighten the uncertainty principle in the presencs of quantum, memory [J]. Phys. Rev. A 2012,86:042105.
[117]E. Ferraro, M. Scala, R. Migliore and A. Napoli, Non-Markovian dissipative dy-namics of two coupled qubits in independent reservoirs:Comparison between exact solutions and master-equation approaches[J]. Phys. Rev. A 2009,80:042112.
[118]I. Sinayskiy, E. Ferraro, A. Napoli, A. Messina and F. Petruccione, Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths[J]. J. Phys. A:Math. Theor.2009,42:485301.
[119]A. S(?)rensen. L. Duan, J. Cirac and P. Zoller, Many-parlicle entanglement with Bose-Einstein condensates[J]. Nature 2001,409:63.
[120]A. D. Cronin, J. Schmiedmayer and D. E. Pritchard, Optics and interferometry with atoms and molecules[J]. Rev. Mod. Phys.2009.81:1051.
[121]X. L. Yin, J. Ma, X. G. Wang and F. Nori, Spin Squeezing under Non-Markovian Channels by Hierarchy Equation Method[J].2012, e-print arXiv:1204.0093
[122]T. C. Wei, K. Nemoto, P. M. Goldbart, P. G. Kwiat, W. J.Munro and F. Ver-straete, Maximal entanglement versus entropy for mixed quantum states[J]. Phys. Rev. A 2003,67:022110.
[123]E. Schrodinger, The Present Status of Quantum Mechanics[J]. Naturwis-senschaften.1935,23:807.
[124]J. M. Raimond, M. Brune and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity [J]. Rev. Mod. Phys.2001,73:565.
[125]B. Julsgaard, A. Kozhekin and E. S. Polzik, Experimental long-lived entanglement of two macroscopic objects[J]. Nature 2001,413:400.
[126]B. B. Blinov, D. L. Moehring, L.-M. Duan and C. Monroe, Observation of entan-glement between a single trapped atom and a single photon[J]. Nature 2004,428: 153.
[127]S. Haroche and J. M. Raimond, Exploring the Quantum:Atoms, Cavities, and Photons[M]. Oxford University Press, Oxford, New York,2006.
[128]H. P. Breuer and J. Piilo, Stochastic Jump Processes for Non-Markovian Quantum Dynamics[J].Europhys. Lett.2009,85:50004.
[129]J. Piilo, S. Maniscalco, K. Harkonen and K. A. Suominen, Non-Markovian Quan-tum Jumps[J]. Phys. Rev. Lett.2008,100:180402.
[130]L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen and B. M. Garraway, Sudden Death and Sudden Birth of Entanglement in Common Structured Reservoirs[J]. Phys. Rev. A 2009,79:042302.
[131]Y. Li, J. Zhou and H. Guo, Effect of the Dipole-Dipole Interaction for Two Atoms with Different Couplings in a Non-Markovian Environment[J]. Phys. Rev. A 2009,79:012309.
[132]J. H. An and W. M. Zhang, Non-Markovian Entanglement Dynamics of Noisy Continuous-Variable Quantum Channels[J]. Phys. Rev. A 2007,76:042127.
[133]Q. J. Tong, J. H. An, H. G. Luo and C. H. Oh, Mechanism of Entanglement Preservation[J]. Phys. Rev. A 2010,81:052330.
[134]X. F. Cao and H. Zheng, Non-Markovian Disentanglement Dynamics of a Two-Qubit System[J]. Phys. Rev. A 2008,77:022320.
[135]Y. J. Zhang, Z. X. Man, X. B. Zou, Y. J. Xia and G. C. Guo, Dynamics of Multipartite Entanglement in the Non-Markovian Environments[J]. J. Phys. B: At. Mol. Opt. Phys.2010,43:,045502.
[136]Z. Y. Xu and M. Feng, Sudden Death and Birth of Entanglement Beyond the Markovian Approximation[J]. Phys. Lett. A 2009,373:1906.
[137]X. Xiao, M.-F. Fang and Y.-L. Li, Non-Markovian Dynamics of Two Qubits Driv-en by Classical Fields.-Population Trapping and Entanglement Preservation[J].J. Phys. B:At. Mol. Opt. Phys.2010,43:185505.
[138]E. T. Jaynes and F. W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser[J]. Proc. IEEE 1963,51: 89.
[139]C. K. Law and J. H. Eberly, Arbitrary Control of a Quantum Electromagnetic Field[J]. Phys. Rev. Lett.1996,76:1055.
[140]F. W. Strauch, K. Jacobs and R. W. Simmonds, Arbitrary Control of Entangle-ment between two Superconducting Resonators[J]. Phys. Rev. Lett.2010,105: 050501.
[141]A. M. Childs and I. L. Chuang, Universal quantum computation with two-level trapped ions[J]. Phys. Rev. A 2000,63:012306.
[142]A. Ben-Kish, B. DeMarco, V. Meyer, M. Rowe, J. Britton, W. M. Itano, B. M. Jelenkovi, C. Langer, D. Leibfried, T. Rosenband and D. J. Wineland, Experimen-tal Demonstration of a Technique to Generate Arbitrary Quantum Superposition States of a Harmonically Bound Spin-1/2 Particle[J]. Phys. Rev. Lett.2003, 90:037902.
[143]F. W. Strauch, D. Onyango, K. Jacobs and R. W. Simmonds, Entangled-state synthesis for superconducting resonators[J]. Phys. Rev. A 2012,85:022335.
[144]E. Brion, K. Mo(?)lmer and M. Saffman, Quantum Computing with Collective En-sembles of Multilevel Systems[J]. Phys. Rev. Lett.2007,99:260501.
[145]M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo and K.-A. Suominen, Population trapping due to cavity losses[J]. Phys. Rev. A 2008,77:043827.
[146]M. Scala, B. Militello, A. Messina, J. Piilo and S. Maniscalco, Microscopic deriva-tion of the Jaynes-Cummings model with cavity losses[J]. Phys. Rev. A 2007, 75:013811.
[147]A. Zeilinger, M.A. Horne, H. Weinfurter and M. Zukowski, Three-Particle Entan-glements from Two Entangled Pairs [J]. Phys. Rev. Lett.1997,78:3031.
[148]S. Bose, V. Vedral and P.L. Knight, Multiparticle generalization of entanglement swapping[J]. Phys. Rev. A 1998,57:822.
[149]J-W. Pan, D. Bouwmeester, H. Weinfurter and A. Zeilinger, Experimental En-tanglement Swapping:Entangling Photons That Never Interacted[J]. Phys. Rev. Lett.1998,80:3891.
[150]M. Zukowski, A. Zeilinger, M.A. Horne and A.K. Ekert, "Event-ready-detectors" Bell experiment via entanglement swapping[J]. Phys. Rev. Lett.1993,71:4287.
[151]L. Wang, S. S. Li and H. Z. Zheng, Conditions for the local manipulation of tripartite Gaussian states[J]. Phys. Rev. A 2003,67:062317.
[152]S. Pirandola, D. Vitali, P. Tombesi and S. Lloyd, Macroscopic Entanglement by Entanglement Swapping[J]. Phys. Rev. Lett.2006,97:150403.
[153]E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat and H. S. Eisenberg, En-tanglement Swapping between Photons that have Never Coexisted[J]. Phys. Rev. Lett.2013,110:210403.
[154]P. Domokos,.T.M. Raimond, M. Brune and S. Haroche, Simple cavity-QED two-bit universal quantum logic gate:The principle and expected performances [J]. Phys. Rev. A 1995,52:3554.
[155]A. Beige. D. Braun, B. Tregenna and P. L. Knight, Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace[J]. Phys. Rev. Lett.2000, 85:1762.
[156]M.E. Tasggin and P. Meystre, Spin squeezing with coherent light via entanglement swapping[J]. Phys. Rev. A 2011,83:053848.
[157]A. Datta, A. Shaji and C. M. Caves, Quantum discord and the Power of One Qubit[J]. Phys. Rev. Lett.2008,100:050502.
[158]A. Datta and S. Gharibian, Signatures of Nonclassicality in Mixed-State Quantum Computation[J]. Phys. Rev. A 2009,79:042325.
[159]J. Cui and H. Fan, Correlations in the Grover Search[J]. J. Phys. A:Math. Theor.2010,43:045305.
[160]R. Dillenschneider, Quantum discord and Quantum Phase Transition in Spin Chains[J]. Phys. Rev. B 2008,78:224413.
[161]M. S. Sarandy. Classical Correlation and Quantum discord in Critical Systems[J]. Phys. Rev. A 2009,80:022108.
[162]B. Wang, Z.-Y. Xu, Z.-Q. Chen and M. Feng, Non-Markovian effect on the quan-tum discord [J]. Phys. Rev. A 2010,81:014101.
[163]F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda and A.O. Caldeira, Non-Markovian dynamics of quantum discord[J]. Phys. Rev. A 2010,81:052107.
[164]X. Xiao, M.F. Fang and Y.L. Li, Quantum discord in Non-Markovian Environ-ments[J]. Opt. commun.2010,283:3001.
[165]Z.-K. Su and S.-J. Jiang, Quantum discord dynamics in structured reservoirs[J]. 2011, e-print arXiv:1105.4911.
[166]C.E. Shannon and W. Weaver, The Mathematical Theory of Communication[M]. Urbana:University of Illinois Press,1949.
[167]T.M. Cover and J.A. Thomas, Eliments of Information Theory[M]. New York:J. Wiley,1991.
[168]C.-Z.Wang, C.-X.Li, L.-Y.Nie and J.-F.Li, Classical correlation and quantum dis-cord mediated by cavity in two coupled qubits[J]. J. Phys. B:At. Mol. Phys. 2011,44:015503.
[169]S. John and J. Wang, Quantum electrodynamics near a photonic band gap:Photon bound states and dressed atoms[J]. Phys. Rev. Lett.1990,64:2418.
[170]S. John and T. Quang, Spontaneous emission near the edge of a photonic band gap[J]. Phys. Rev. A 1994,50:1764.
[171]T. Quang, M. Woldeyohannes, S. John and G. S. Agarwal, Coherent Control of Spontaneous Emission near a Photonic Band Edge:A Single-Atom Optical Memory Device[J]. Phys. Rev. Lett.1997,79:5238.
[2]C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters. Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels[J]. Phys. Rev. Lett.1993,70:1895.
[3]D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger, Experimental Quantum Teleportation[J]. Nature,1997,390:575.
[4]M. Keyl, Fundamentals of Quantum Information Theory[J]. Phys. Rep.2002, 369:431.
[5]G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rotteler, H. Weinfurter, R. Werner and A. Zeilinger, Quantum Information:An Introduction to Basic Theoretical Concepts and Experiments[J]. Beijing:World Publishing Cor-poratin,2004.
[6]V. Vedral, Introdution to Quantum Information Science[M]. Oxford:Oxford Uni-versity Press,2006.
[7]L. Amico, R. Fazio, A. Osterloh and V. Vedral, Entanglement in Many-Body Systems[J]. Rev. Mod. Phys.2008,80:517.
[8]H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems[M]. Ox-ford:Oxford University Press,2007.
[9]C. W. Gardiner and P. Zoller,Quantum Noise[M]. Berlin:Springer-Verlag Press, 1999.
[10]U. Weiss, Quantum Dissipative Systems[M]. Singapore:World Scientific Press, 2008.
[11]B. J. Dalton, S. M. Barnett and B. M. Garraway, Theory of Pseudom.odes in Quantum Optical Processes [J]. Phys. Rev. A 2001,64:053813.
[12]A. Wallraff, et.al., Strong coupling of a single photon to a superconducting qubit using circuit quantumelectrodynamics[J]. Nature 2004,431:162.
[13]J. P. Reithmaier et al., Strong coupling in a single quantum dot-semiconductor microcavity system[J]. Nature 2004,432:197.
[14]P. Lambropoulos et al., Fundamental quantum optics in structured reservoirs[J]. Rep. Prog. Phys.2000,63:455.
[15]C. W. Lai, P. Maletinsky, A. Badolato and A. Imamoglu, Knight-Field-Enabled Nuclear Spin Polarization in Single Quantum Dots[J]. Phys. Rev. Lett.2006, 96:167403.
[16]A. Pomyalov and D. J. Tannor, The non-Markovian quantum master equation in the collective-mode representation:Application to barrier crossing in the interme-diate friction regime[J]. J. Chem. Phys.2005,123:204111.
[17]Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger and J. Reichel, Strong Atom-Field Coupling for Bose-Einstein Condensates in an Optical Cavity on a Chip[J]. Nature 2007,450:272.
[18]K. Hennessy, et. al., Quantum nature of a strongly coupled single quantum dot-cavity system[J]. Nature 2007,445:896.
[19]W. Heisenberg, Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[J]. Z. Phys.1927,43:172.
[20]I. Bialynicki-Birula, Entropic uncertainty relations[J]. Phys. Lett. A 1984,103: 253.
[21]I. Bialynicki-Birula and J. L. Madajczyk, Entropic uncertainty relations for angu-lar distributions[J]. Phys. Lett. A 1985,108:384.
[22]J. A. Vaccaro and R. F. Bonner, Pegg-Barnett phase operators of infinite rank[J]. Phys. Lett. A 1995,198:167.
[23]I. I. Hirschman, A note on entropy[J]. Amer. J. Math.1957,79:152.
[24]D. Deutsch, Uncertainty in Quantum Measurements[J]. Phys. Rev. Lett.1983, 50:631.
[25]K. Kraus, Complementary observables and uncertainty relations[J]. Phys. Rev. D 1987,35:3070.
[26]H. Maassen and J. B. Uffink, Generalized entropic uncertainty relations[J]. Phys. Rev. Lett.1988,60:1103.
[27]J. Sanchez-Ruiz, Entropic uncertainty and certainty relations for complementary observables[J]. Phys. Lett. A 1993,173:233.
[28]J. M. Renes and J.-C. Boilean, Conjectured Strong Complementary Information Tradeoff[J]. Phys. Rev. Lett.2009,103:020402.
[29]M. Berta,M.Christandl, R. Colbeck, J. M. Renes and B.Benner, The Uncertainty Principle in the Presence of Quantum Memory[J]. Nat. Phys.2010,6:659.
[30]R. Prevedel, D. R. Hamel, R. Colbeck, K. Fisher and K. J. Resch, Experimental investigation of the uncertainty principle in the presence of quantum memory[J]. Nat. Phys.2011,7:757.
[31]C. F. Li, J. S. Xu, X. Y. Xu, K. Li and G. C. Guo, Experimental investigation of the entanglement-assisted entropic uncertainty principle[J]. Nat. Phys.2011,7: 752.
[32]M. Tomamichel, C. C. W. Lim, N. Gisin and R. Renner, Tight Finite-Key Analysis for Quantum Cryptography[J]. Nature Commun.2012,3:634.
[33]D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin and B. M. Terhal, Locking classical correlations in quantum states[J]. Phys. Rev. Lett.2004,92: 067902.
[34]P. Nataf, M. Dogan and K. L. Hur, Heisenberg uncertainty principle as a probe of entanglement entropy:Application to superradiant quantum phase transitions[J]. Phys. Rev. A 2012,86:043807.
[35]M.-L. Hu and H. Fan, Quantum-memory-assisted, entropic uncertainty principle. teleportation. and entanglement witness in structured reservoirs[J]. Phys. Rev. A 2012,86:032338.
[36]G. M. Gaves, Quantum-mechanical noise in an interferometer[J]. Phys. Rev. D 1981,23:1693.
[37]R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Quantum Eentan-glement[J]. Rev. Mod. Phys.2009,81:865.
[38]O. Guehne and G. Toth, Entanglement detection[J]. Phys. Rep.2009,474:1.
[39]S. L. Braunstein and P. van Loock, Quantum information with continuous vari-ables[J]. Rev. Mod. Phys.2005,77:513.
[40]I. D. Leroux, M. H. Schleier-Smith and V. Vuletic, Implementation of Cavity Squeezing of a Collective Atomic Spin[J]. Phys. Rev. Lett.2010,104:073602.
[41]D. J. Wineland, J. J. Bollonger and W. M. Itano, Squeezed atomic states and projection noise in spectroscopy[J]. Phys. Rev. A 1994,50:67.
[42]K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari,K. Mckenzie, R. Ward, S. Vass, A. J. Weinstein and N. Mavalvala, A quantum-enhanced prototype gravitational-wave detector[J].Nat. Phys.2008,4:472.
[43]J. A. Dunningham and K. Burnett, Sub-shot-noise-limited measurements with Bose-Einstein condensates[J]. Phys. Rev. A 2004,70:033601.
[44]M. Kitagawa and M. Ueda, Squeezed spin states[J]. Phys. Rev. A 1993,47: 5138.
[45]J.-Ma, X.-G. Wang, C. P. Sun and Franco Nori, Quantum spin squeezing[J]. Phys. Rep.2011,509:89.
[46]X. Wang and B. C. Sanders, Spin squeezing and pairwise entanglement for sym-metric multiqubit states[J]. Phys. Rev. A 2003,68:012101.
[47]A. S(?)rensen and K. M(?)lmer, Spin-Spin Interaction and Spin Squeezing in an Op-tical Lattice[J]. Phys. Rev. Lett.1999,83:2274.
[48]G. Toth, C. Knapp,O. Giihne, and H. J. Briegel, Optimal Spin Squeezing Inequal-ities Detect Bound Entanglement in Spin Models[J]. Phys. Rev. Lett.2007,99: 250405.
[49]G. T6th,C. Knapp, O. Giihne, and H. J. Briegel, Spin squeezing and entanglemen-t[J]. Phys. Rev. A 2009,79:042334.
[50]E. Knill and R. Laflamme, Power of One Bit of Quantum Information[J]. Phys. Rev. Lett.1998,81:5672.
[51]N. Gisin and R. Thew, Quantum Communication[J]. Nat. Photonics 2007,1: 165.
[52]S. Lloyd, Universal Quantum Simulators[J]. Science 1996,273:1073.
[53]M. F. Santos, P. Milman, L. Davidovich and N. Zagury, Direct measurement of finite-time disentanglement induced by a reservoir[J]. Phys. Rev. A 2006,73: 040305(R).
[54]T. Yu and J. H. Eberly, Finite-Time Disentanglement Via Spontaneous Emis-sion[J]. Phys. Rev. Lett.2004,93:140404.
[55]T. Yu and J.H. Eberly, Sudden death of entanglement[J]. Science 2009,323:598.
[56]M. P. Almeida et al., Experimental Observation OF Finite-Time Disentanglemen-t[J]. Science 2007,316:579.
[57]B. Bellomo, R. Lo Franco and G. Compagno, Non-Markovian Effects on the Dy-namics of Entanglement[J]. Phys. Rev. Lett.2007,99:160502.
[58]B. Bellomo, R. Lo Franco and G. Compagno, Entanglement dynamics of two independent qubits in environments with and without memory [J]. Phys. Rev. A 2008,77:032342.
[59]B. Bellomo, R. Lo Franco, S. Maniscalco and G. Compagno, Entanglement Trap-ping in Structured Environments[J]. Phys. Rev. A 2008,78:060302(R).
[60]M. Ban, S. Kitajima and F. Shibata, Decoherence of quantum information in the non-Markovian qubit channel[J]. J. Phys. A:Math. Gen.2005,38:7161.
[61]E. Bihama,G. Brassardb, D. Kenigsberga and T. Mor, Quantum, Computing With-out Entanglement[J]. Theor. Comput. Sci.2004,320:15.
[62]L. Henderson and V. Vedral, Classical. Quantum and Total Correlations[J]. J. Phys. A:Math. Theor.2001,34:6899.
[63]H. Ollivier and W. H. Zurek, Quantum discord:A Measure of the Quantumness of Correlations[J]. Phys. Rev. Lett.2001,88:017901.
[64]B. P. Lanyon, M. Barbieri, M. P. Almeida and A. G. White, Experimental Quan-tum Computing without, Entanglement[J]. Phys. Rev. Lett.2008,101:200501.
[65]P. Giorda and M. G. A. Paris, Gaussian Quantum discord [J]. Phys. Rev. Lett. 2010,105:020503.
[66]D. Cavalcanti, L. Aolita, S. Boixo, K. Modi, M. Piani and A. Winter, Operational Interpretations of Quantum. discord[J]. Phys. Rev. A 2011,83:032324.
[67]S. Luo and S. Fu, Geometric Measure of Quantum discord[J]. Phys. Rev. A 2010, 82:034302.
[68]S. Luo, Quantum discord for Two-Qubit Systems[J]. Phys. Rev. A 2008,77: 042303.
[69]C. C. Rulli and M. S. Sarandy, Global Quantum discord in Multipartite Systems[J]. Phys. Rev. A 2011,84:042109.
[70]L. Ciliberti, R. Rossignoli, and N. Canosa, Quantum discord in Finite XY Chain-s[J]. Phys. Rev. A 2010,82:042316.
[71]B. Li, Z. X. Wang and S. M. Fei, Quantum discord and Geometry for a Class of Two-Qubit States[J]. Phys. Rev. A 2010,83:022321.
[72]C K. Lee, L. C. Kwek and J. Cao, Stochastic Resonance of Quantum discord[J]. Phys. Rev. A 2011,84:062113.
[73]C. Zhang, S. Yu, Q. Chen and C. H. Oh, Detecting the Quantum discord of an Unknown State by a Single Observable[J]. Phys. Rev. A 2011,84:032122.
[74]A. Streltsov, H. Kampermann, and D. Brufβ, Behavior of Quantum Correlations under Local Noise[J]. Phys. Rev. Lett.2011,107:170502.
[75]H. I. Yoo and J. H. Eberly, Dynamical theory of an atom with two or three levels interacting with quantized cavity fields Review Article[J]. Phys. Rep.1985,118: 239.
[76]P. M. Radmore, Population trapping in a multilevel system[J]. Phys. Rev. A 1982,26:2252.
[77]Z. Deng and J. H. Eberly, Coherent trapping in continuum-continuum transition-s[J]. Phys. Rev. A 1986,34:2492.
[78]J. I. Cirac and L. L. Sanchez-Soto, Population trapping in the Jaynes-Cummings model via phase coupling[J]. Phys. Rev. A 1990,42:2851.
[79]J. I. Cirac and L.L. Sanchez-Soto, Population trapping in two-level models:Spectral and statistical properties[J]. Phys. Rev. A 1991,44:3317.
[80]G. S. Agarwal, Coherent population trapping states of a system interacting with quantized fields and the production of the photon statistics matched fields[J]. Phys. Rev. Lett.1993,71:1351.
[81]W. D. Phillips, Laser cooling and trapping of neutral atoms[J]. Rev. Mod. Phys. 1998,70:721.
[82]K. Bergmann, H. Theuer and B. W. Shore, Coherent population transfer among quantum states of atoms and molecules[J]. Rev. Mod. Phys.1998,70:1003.
[83]P. Kral, I. Thanopulos and M. Shapiro, Colloquium:Coherently controlled adia-batic passage[J]. Rev. Mod. Phys.2007,79:53.
[84]M. Fleischhauer, A. Imamoglu and J. P. Marangos, Electromagnetically induced transparency:Optics in coherent media [J]. Rev. Mod. Phys.2005,77:633.
[85]M. D. Lukin, Colloquium:Trapping and manipulating photon states in atomic ensembles[J]. Rev. Mod. Phys.2003,75:457.
[86]J. Mompart and R. Corbalan, Lasing without inversion[J]. J. Opt. B:Quantum Semiclass. Opt.2000,2:R7.
[87]B. Lev et al, Feasibility of detecting single atoms using photonic bandgap cavi-ties[J]. Nanotechnology 2004,15:S556.
[88]L. Florescu, S. John, T. Quang and R. Wang, Theory of a one-atom laser in a photonic band-gap microchip[J]. Phys. Rev. A 2004,69:013816.
[89]肖兴,开放量子系统的非马尔科夫动力学和弱测量反馈控制[D].湖南：湖南师范大学博士学位论文,2012.
[90]W. H. Zurek, Decoherence, Einselection. and the Quantum Origins of the Classi-cal[J]. Rev. Mod. Phys.2003,75:715.
[91]曾谨言,量子力学[M].北京：科学出版社,2001.
[92]K. Hornberger, Introduction to Decoherence Theory[J]. Lect. Notes Phys.2009, 768:221.
[93]G. Landblad, On the Generators of Quantum Dynamical Semigroups[J]. Com-mun. Math. Phys.1976,48:119.
[94]W. H. Louisell, Quantum Statistical Properties of Radiation[M]. New York:Wiley, 1973.
[95]S. Nakajima, On Quantum Theory of Transport Phenomena[J]. Prog. Theor. Phys.1958,20:948.
[96]R. Zwanzig, Ensemble Method in the Theory of Irreversibility[J]. J. Chem. Phys. 1960,33:1338.
[97]S. Chaturvedi and F. Shibata, Time-Convolutionless Projection Operator Formal-ism for Elimination of Fast Variables:Applications to Brownian Motion[J]. Z. Phys. B 1979,35:297.
[98]H.-P. Breuer, B. Kapplera and F. Petruccionea, The Time-Convolutionless Pro-jection Operator Technique in the Quantum Theory of Dissipation and Decoher-ence[J]. Ann. Phys.2002,291:36.
[99]A. Shabani and D. A. Lidar, Completely Positive Post-Markovian Master Equation via a Measurement Approach[J]. Phys. Rev. A 2005,71:020101(R).
[100]G. Schaller and T. Brandes, Preservation of Positivity by Dynamical Coarse Grain-ing[J]. Phys. Rev. A 2008,78:022106.
[101]M. M. Jack, Non-Markovian Quantum Trajectories[D]. University of Auckland, PhD Thesis,1999.
[102]I. Bialynicki-birula and J. Mycielski, Uncertainty relations for information entropy in wave mechanics[J]. Commun. Math. Phys.1975,44:129.
[103]Y.-K. Kim and Y. Shih, Experimental realization of Popper's Experiment:Viola-tion of the Uncertainty Principle[J]. Found. Phys.1999,29:1849.
[104]H. F. Hofmann and S. Takeuchi, Violation of local uncertainty relations as a sig-nature of entanglement[J]. Phys. Rev. A 2003,68:032103.
[105]I. Devetak and A. Winter, Distillation of secret key and entanglement from quan-tum states[J]. Proc. R. Soc. A 2005,461:207.
[106]彭金生,李高翔,近代量子光学导论[M].北京：科学出版社,1996.
[107]D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy[J]. Phys. Rev. A 1992,46: R6797.
[108]X. Xiao, M. F. Fang and Y. M. Hu, Protecting Atomic Squeezing by Detuning in Non-Markovian Environments[J]. Phys. Scr.2011,84:045011.
[109]L. Henderson and V. Vedral, Information, Relative Entropy of Entanglement, and Irreversibility[J]. Phys. Rev. Lett.2000,84:2263.
[110]S. Bose and V. Vedral, Mixedness and teleportation[J]. Phys. Rev. A.2000,61: 040101(R).
[111]P. Horodecki, Separability criterion and inseparable mixed states with positivepar-tial transposition[J]. Phys. Lett. A 1997,232:333.
[112]W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubit-s[J]. Phys. Rev. Lett.1998,80:2245.
[113]K. Modi, T. Paterek, W. Son, V. Vedral and M. Williamson, Unified View of Quantum and Classical Correlations[J]. Phys. Rev. Lett.2010,104:080501.
[114]B. Dakic, V. Vedral and C. Brukner, Necessary and Sufficient Condition for Nonzero Quantum discord[J]. Phys. Rev. Lett.2010,105:190502.
[115]Z.-Y. Xu, W. L. Yang and M. Feng, Quantum-memory-assisted entropic uncer-tainty relation under noise[J]. Phys. Rev. A 2012,86:012113.
[116]A. K. Pati, M. M. Wilde, A. R. Usha Devi, A. K. Rajagopal and Sudha, Quan-tum discord and classical correlation can tighten the uncertainty principle in the presencs of quantum, memory [J]. Phys. Rev. A 2012,86:042105.
[117]E. Ferraro, M. Scala, R. Migliore and A. Napoli, Non-Markovian dissipative dy-namics of two coupled qubits in independent reservoirs:Comparison between exact solutions and master-equation approaches[J]. Phys. Rev. A 2009,80:042112.
[118]I. Sinayskiy, E. Ferraro, A. Napoli, A. Messina and F. Petruccione, Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths[J]. J. Phys. A:Math. Theor.2009,42:485301.
[119]A. S(?)rensen. L. Duan, J. Cirac and P. Zoller, Many-parlicle entanglement with Bose-Einstein condensates[J]. Nature 2001,409:63.
[120]A. D. Cronin, J. Schmiedmayer and D. E. Pritchard, Optics and interferometry with atoms and molecules[J]. Rev. Mod. Phys.2009.81:1051.
[121]X. L. Yin, J. Ma, X. G. Wang and F. Nori, Spin Squeezing under Non-Markovian Channels by Hierarchy Equation Method[J].2012, e-print arXiv:1204.0093
[122]T. C. Wei, K. Nemoto, P. M. Goldbart, P. G. Kwiat, W. J.Munro and F. Ver-straete, Maximal entanglement versus entropy for mixed quantum states[J]. Phys. Rev. A 2003,67:022110.
[123]E. Schrodinger, The Present Status of Quantum Mechanics[J]. Naturwis-senschaften.1935,23:807.
[124]J. M. Raimond, M. Brune and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity [J]. Rev. Mod. Phys.2001,73:565.
[125]B. Julsgaard, A. Kozhekin and E. S. Polzik, Experimental long-lived entanglement of two macroscopic objects[J]. Nature 2001,413:400.
[126]B. B. Blinov, D. L. Moehring, L.-M. Duan and C. Monroe, Observation of entan-glement between a single trapped atom and a single photon[J]. Nature 2004,428: 153.
[127]S. Haroche and J. M. Raimond, Exploring the Quantum:Atoms, Cavities, and Photons[M]. Oxford University Press, Oxford, New York,2006.
[128]H. P. Breuer and J. Piilo, Stochastic Jump Processes for Non-Markovian Quantum Dynamics[J].Europhys. Lett.2009,85:50004.
[129]J. Piilo, S. Maniscalco, K. Harkonen and K. A. Suominen, Non-Markovian Quan-tum Jumps[J]. Phys. Rev. Lett.2008,100:180402.
[130]L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen and B. M. Garraway, Sudden Death and Sudden Birth of Entanglement in Common Structured Reservoirs[J]. Phys. Rev. A 2009,79:042302.
[131]Y. Li, J. Zhou and H. Guo, Effect of the Dipole-Dipole Interaction for Two Atoms with Different Couplings in a Non-Markovian Environment[J]. Phys. Rev. A 2009,79:012309.
[132]J. H. An and W. M. Zhang, Non-Markovian Entanglement Dynamics of Noisy Continuous-Variable Quantum Channels[J]. Phys. Rev. A 2007,76:042127.
[133]Q. J. Tong, J. H. An, H. G. Luo and C. H. Oh, Mechanism of Entanglement Preservation[J]. Phys. Rev. A 2010,81:052330.
[134]X. F. Cao and H. Zheng, Non-Markovian Disentanglement Dynamics of a Two-Qubit System[J]. Phys. Rev. A 2008,77:022320.
[135]Y. J. Zhang, Z. X. Man, X. B. Zou, Y. J. Xia and G. C. Guo, Dynamics of Multipartite Entanglement in the Non-Markovian Environments[J]. J. Phys. B: At. Mol. Opt. Phys.2010,43:,045502.
[136]Z. Y. Xu and M. Feng, Sudden Death and Birth of Entanglement Beyond the Markovian Approximation[J]. Phys. Lett. A 2009,373:1906.
[137]X. Xiao, M.-F. Fang and Y.-L. Li, Non-Markovian Dynamics of Two Qubits Driv-en by Classical Fields.-Population Trapping and Entanglement Preservation[J].J. Phys. B:At. Mol. Opt. Phys.2010,43:185505.
[138]E. T. Jaynes and F. W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser[J]. Proc. IEEE 1963,51: 89.
[139]C. K. Law and J. H. Eberly, Arbitrary Control of a Quantum Electromagnetic Field[J]. Phys. Rev. Lett.1996,76:1055.
[140]F. W. Strauch, K. Jacobs and R. W. Simmonds, Arbitrary Control of Entangle-ment between two Superconducting Resonators[J]. Phys. Rev. Lett.2010,105: 050501.
[141]A. M. Childs and I. L. Chuang, Universal quantum computation with two-level trapped ions[J]. Phys. Rev. A 2000,63:012306.
[142]A. Ben-Kish, B. DeMarco, V. Meyer, M. Rowe, J. Britton, W. M. Itano, B. M. Jelenkovi, C. Langer, D. Leibfried, T. Rosenband and D. J. Wineland, Experimen-tal Demonstration of a Technique to Generate Arbitrary Quantum Superposition States of a Harmonically Bound Spin-1/2 Particle[J]. Phys. Rev. Lett.2003, 90:037902.
[143]F. W. Strauch, D. Onyango, K. Jacobs and R. W. Simmonds, Entangled-state synthesis for superconducting resonators[J]. Phys. Rev. A 2012,85:022335.
[144]E. Brion, K. Mo(?)lmer and M. Saffman, Quantum Computing with Collective En-sembles of Multilevel Systems[J]. Phys. Rev. Lett.2007,99:260501.
[145]M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo and K.-A. Suominen, Population trapping due to cavity losses[J]. Phys. Rev. A 2008,77:043827.
[146]M. Scala, B. Militello, A. Messina, J. Piilo and S. Maniscalco, Microscopic deriva-tion of the Jaynes-Cummings model with cavity losses[J]. Phys. Rev. A 2007, 75:013811.
[147]A. Zeilinger, M.A. Horne, H. Weinfurter and M. Zukowski, Three-Particle Entan-glements from Two Entangled Pairs [J]. Phys. Rev. Lett.1997,78:3031.
[148]S. Bose, V. Vedral and P.L. Knight, Multiparticle generalization of entanglement swapping[J]. Phys. Rev. A 1998,57:822.
[149]J-W. Pan, D. Bouwmeester, H. Weinfurter and A. Zeilinger, Experimental En-tanglement Swapping:Entangling Photons That Never Interacted[J]. Phys. Rev. Lett.1998,80:3891.
[150]M. Zukowski, A. Zeilinger, M.A. Horne and A.K. Ekert, "Event-ready-detectors" Bell experiment via entanglement swapping[J]. Phys. Rev. Lett.1993,71:4287.
[151]L. Wang, S. S. Li and H. Z. Zheng, Conditions for the local manipulation of tripartite Gaussian states[J]. Phys. Rev. A 2003,67:062317.
[152]S. Pirandola, D. Vitali, P. Tombesi and S. Lloyd, Macroscopic Entanglement by Entanglement Swapping[J]. Phys. Rev. Lett.2006,97:150403.
[153]E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat and H. S. Eisenberg, En-tanglement Swapping between Photons that have Never Coexisted[J]. Phys. Rev. Lett.2013,110:210403.
[154]P. Domokos,.T.M. Raimond, M. Brune and S. Haroche, Simple cavity-QED two-bit universal quantum logic gate:The principle and expected performances [J]. Phys. Rev. A 1995,52:3554.
[155]A. Beige. D. Braun, B. Tregenna and P. L. Knight, Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace[J]. Phys. Rev. Lett.2000, 85:1762.
[156]M.E. Tasggin and P. Meystre, Spin squeezing with coherent light via entanglement swapping[J]. Phys. Rev. A 2011,83:053848.
[157]A. Datta, A. Shaji and C. M. Caves, Quantum discord and the Power of One Qubit[J]. Phys. Rev. Lett.2008,100:050502.
[158]A. Datta and S. Gharibian, Signatures of Nonclassicality in Mixed-State Quantum Computation[J]. Phys. Rev. A 2009,79:042325.
[159]J. Cui and H. Fan, Correlations in the Grover Search[J]. J. Phys. A:Math. Theor.2010,43:045305.
[160]R. Dillenschneider, Quantum discord and Quantum Phase Transition in Spin Chains[J]. Phys. Rev. B 2008,78:224413.
[161]M. S. Sarandy. Classical Correlation and Quantum discord in Critical Systems[J]. Phys. Rev. A 2009,80:022108.
[162]B. Wang, Z.-Y. Xu, Z.-Q. Chen and M. Feng, Non-Markovian effect on the quan-tum discord [J]. Phys. Rev. A 2010,81:014101.
[163]F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda and A.O. Caldeira, Non-Markovian dynamics of quantum discord[J]. Phys. Rev. A 2010,81:052107.
[164]X. Xiao, M.F. Fang and Y.L. Li, Quantum discord in Non-Markovian Environ-ments[J]. Opt. commun.2010,283:3001.
[165]Z.-K. Su and S.-J. Jiang, Quantum discord dynamics in structured reservoirs[J]. 2011, e-print arXiv:1105.4911.
[166]C.E. Shannon and W. Weaver, The Mathematical Theory of Communication[M]. Urbana:University of Illinois Press,1949.
[167]T.M. Cover and J.A. Thomas, Eliments of Information Theory[M]. New York:J. Wiley,1991.
[168]C.-Z.Wang, C.-X.Li, L.-Y.Nie and J.-F.Li, Classical correlation and quantum dis-cord mediated by cavity in two coupled qubits[J]. J. Phys. B:At. Mol. Phys. 2011,44:015503.
[169]S. John and J. Wang, Quantum electrodynamics near a photonic band gap:Photon bound states and dressed atoms[J]. Phys. Rev. Lett.1990,64:2418.
[170]S. John and T. Quang, Spontaneous emission near the edge of a photonic band gap[J]. Phys. Rev. A 1994,50:1764.
[171]T. Quang, M. Woldeyohannes, S. John and G. S. Agarwal, Coherent Control of Spontaneous Emission near a Photonic Band Edge:A Single-Atom Optical Memory Device[J]. Phys. Rev. Lett.1997,79:5238.