连续变量纠缠在原子和磁振子系统中的理论研究
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摘要
量子信息学作为新兴学科在国际上兴起是在1994年之后，虽然时间很短，但已取得一系列的重要突破。量子信息学主要包括了量子信息论、量子通信、量子光通信和量子算法与量子计算等等。近年来，量子信息在理论上和实验上都取得了重大进展，已经引起各国政府、科学界和信息产业界的高度重视。量子纠缠是量子信息学中最基础、最核心的部分，其作为几乎所有量子信息处理任务中都不可缺少的物理资源，吸引了众多物理学家的巨大兴趣。近来，有关连续变量纠缠态的制备及其在量子信息处理中的应用成为量子光学和量子信息科学的前沿研究领域。连续变量纠缠态性质的研究不仅可以用于验证量子力学的基本原理，而且还是量子信息处理的基本资源。因此，如何制备出连续变量纠缠态引起了人们的广泛关注。
本论文主要呈现的是几种连续变量系统纠缠性质的理论研究，研究内容分三大部分：
第一部分，利用连续变量系统的双模纠缠判据，分别研究了三能级梯形原子系统的稳态与瞬态的量子纠缠性质。通过在原子的两个能级之间施加一个相干外驱动场，使原子能级之间跃迁的两个不同频率的光场发生纠缠。研究发现泵浦强度、原子与光场之间的耦合系数等对系统的纠缠性质起着积极作用，而失谐量、原子的衰减系数及腔的衰减系数对系统的纠缠性质起着抑制作用。在此基础上，还研究了三能级梯形原子系统中量子纠缠与Bell不等式的违背之间的关系，发现该系统中存在有些量子纠缠态并没有违背Bell不等式。
第二部分，分别研究了反铁磁体与铁磁体中磁振子的纠缠特性。通过求解时间演化算符，得到产生湮灭算符的时间演化关系，然后得到自旋分量的量子涨落表达式。依据量子纠缠判据，研究发现反铁磁体中两束向不同方向传播的自旋波之间会产生周期性的纠缠，铁磁体中沿同方向传播的两束不同能量的自旋波之间也会产生周期性的纠缠。
第三部分，分别研究了压缩相干态与叠加相干态的量子纠缠性质。对于压缩相干态，量子纠缠仅与压缩参数与压缩角有关，与平移参数无关；对于叠加相干态，量子纠缠会受到相干振幅、相位角及相对相位的取值影响。
Quantum informatics as a newly subject didn't rise in the world until 1994. Thoughthe time is short, a series of important breakthroughs have been gained. Quantuminformatics mainly includes quantum information, quantum communication, quantumoptical communication, quantum computation and so on. In recent years, a surprisingprogress on quantum information has been made at the theoretic and experimental fields,which have attracted much attention of the states of all the countries and people who workin the field of science or in the information industries. Quantum entanglement, the core ofthe quantum information theory, attracts much attention from many researchers due to thefact that it is the indispensable physical resource in quantum information processing. Now,continuous variable entanglement has attracted a lot of attention in quantum optics andquantum information due to the experimental realization of quantum informationprocessings in continuous variable regime. Therefore, the preparation of continuousvariable entanglement attracts much attention now.
Entanglement propertities of several continuous variable systems are studied in thisthesis, and the main research contents are as follows:
First, entanglement properties of the steady states and the transient states in acascade three-level atomic system are investigated respectively according to the two-modecontinuous variable criterion. The top and bottom levels of the system are coupled by astrong external pump field. Two different frequency fields that may be entangled can beproduced by the transition from the top to the bottom level via the intermediate level. Wefind that the density of pump field and atom-field coupling constants play the positive rolein entanglement properties, while detuning, damping constant and atom decay rates playthe negative role in entanglement properties. Furthermore, we study the relation betweenquantum entanglement and violation of Bell's inequality in another three-level cascade atomic system. We find there are some states which are entangled do not violate the Bell'sinequality.
Second, the dynamics of entanglement for two-mode magnons in antiferromagnetand ferromagnet is investigated respectively according to the two-mode continuousvariable criterion. We can obtain the time-dependent operators of magnons by the timeevolution operator. The quantum fluctuation expressions of the spin components can alsobe obtained. It is shown that entanglement between the two spin-waves along the oppositedirection can be generated and occurs periodically with time in the antiferromagnet, andentanglement between the two spin-waves along the same direction which has differentenergies can also be generated and occurs periodically with time in the ferromagnet.
Third, entanglement properties of two-mode squeezed coherent states andsuperposition states from several two-mode coherent states in radiation field areinvestigated according to the continuous variable entanglement criteria. It shows that thesqueeze angle and squeeze parameter play an essential role in the study of entanglementproperties for two-mode squeezed coherent states. On the other hand, for superpositionstates from several two-mode coherent states, it is found that the entanglement dependsstrongly on coherent amplitude of each mode, phase angle and relative phase angle.
本论文主要呈现的是几种连续变量系统纠缠性质的理论研究，研究内容分三大部分：
第一部分，利用连续变量系统的双模纠缠判据，分别研究了三能级梯形原子系统的稳态与瞬态的量子纠缠性质。通过在原子的两个能级之间施加一个相干外驱动场，使原子能级之间跃迁的两个不同频率的光场发生纠缠。研究发现泵浦强度、原子与光场之间的耦合系数等对系统的纠缠性质起着积极作用，而失谐量、原子的衰减系数及腔的衰减系数对系统的纠缠性质起着抑制作用。在此基础上，还研究了三能级梯形原子系统中量子纠缠与Bell不等式的违背之间的关系，发现该系统中存在有些量子纠缠态并没有违背Bell不等式。
第二部分，分别研究了反铁磁体与铁磁体中磁振子的纠缠特性。通过求解时间演化算符，得到产生湮灭算符的时间演化关系，然后得到自旋分量的量子涨落表达式。依据量子纠缠判据，研究发现反铁磁体中两束向不同方向传播的自旋波之间会产生周期性的纠缠，铁磁体中沿同方向传播的两束不同能量的自旋波之间也会产生周期性的纠缠。
第三部分，分别研究了压缩相干态与叠加相干态的量子纠缠性质。对于压缩相干态，量子纠缠仅与压缩参数与压缩角有关，与平移参数无关；对于叠加相干态，量子纠缠会受到相干振幅、相位角及相对相位的取值影响。
Quantum informatics as a newly subject didn't rise in the world until 1994. Thoughthe time is short, a series of important breakthroughs have been gained. Quantuminformatics mainly includes quantum information, quantum communication, quantumoptical communication, quantum computation and so on. In recent years, a surprisingprogress on quantum information has been made at the theoretic and experimental fields,which have attracted much attention of the states of all the countries and people who workin the field of science or in the information industries. Quantum entanglement, the core ofthe quantum information theory, attracts much attention from many researchers due to thefact that it is the indispensable physical resource in quantum information processing. Now,continuous variable entanglement has attracted a lot of attention in quantum optics andquantum information due to the experimental realization of quantum informationprocessings in continuous variable regime. Therefore, the preparation of continuousvariable entanglement attracts much attention now.
Entanglement propertities of several continuous variable systems are studied in thisthesis, and the main research contents are as follows:
First, entanglement properties of the steady states and the transient states in acascade three-level atomic system are investigated respectively according to the two-modecontinuous variable criterion. The top and bottom levels of the system are coupled by astrong external pump field. Two different frequency fields that may be entangled can beproduced by the transition from the top to the bottom level via the intermediate level. Wefind that the density of pump field and atom-field coupling constants play the positive rolein entanglement properties, while detuning, damping constant and atom decay rates playthe negative role in entanglement properties. Furthermore, we study the relation betweenquantum entanglement and violation of Bell's inequality in another three-level cascade atomic system. We find there are some states which are entangled do not violate the Bell'sinequality.
Second, the dynamics of entanglement for two-mode magnons in antiferromagnetand ferromagnet is investigated respectively according to the two-mode continuousvariable criterion. We can obtain the time-dependent operators of magnons by the timeevolution operator. The quantum fluctuation expressions of the spin components can alsobe obtained. It is shown that entanglement between the two spin-waves along the oppositedirection can be generated and occurs periodically with time in the antiferromagnet, andentanglement between the two spin-waves along the same direction which has differentenergies can also be generated and occurs periodically with time in the ferromagnet.
Third, entanglement properties of two-mode squeezed coherent states andsuperposition states from several two-mode coherent states in radiation field areinvestigated according to the continuous variable entanglement criteria. It shows that thesqueeze angle and squeeze parameter play an essential role in the study of entanglementproperties for two-mode squeezed coherent states. On the other hand, for superpositionstates from several two-mode coherent states, it is found that the entanglement dependsstrongly on coherent amplitude of each mode, phase angle and relative phase angle.
引文
[1] Braunstein S L, Loock P V. Quantum information with continuous variables. 2005, 77(2): 513-577.
[2] 郭光灿．量子信息引论．见：曾谨言，裴寿镛．99量子力学新进展(第一辑)．北京：北京大学出版社，2000年，249-285．
[3] Michael A, Nielsen, Issac L. Chuang, Quantum computation and quantum information, Cambridge University Press: Cambridge (2000).
[4] Schrodinger E. Die gegenw artige situation in der quantenme chanik [J]. Naturwissenschaften, 1935, 23:807.
[5] Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev, 1935, 47: 777-780.
[6] Bennett C H, Brassard G, Crepeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 1993, 70 (13):1895-1899.
[7] Zheng Y Z, Gu Y J, Guo G C. Teleportation of a three-particle entangled W state. Chin. Phys. 2002, 11 (6):537-542.
[8] Dai H Y, Chen P X, Li C Z. Probabilistic teleportation of an arbitrary two-particle state by two partial three-particle entangled W states. J. Opt. B: Quantum Semiclass. Opt., 2004, 6(1): 106-109.
[9] Zhou L, Kuang L M. Linear optical implementation for quantum teleportation of unknown two-qubit entangled states. Chin. Phys. Lett. 2004, 21 (11): 2101-2104.
[10] Guerra E S. Teleportation of atomic states via cavity quantum electrodynamics. Opt. Commun. 2004, 242(4-6):541-549.
[11] Yan F L, Wang D. Probabilistic and controlled teleportation of unknown quantum states. Phys. Lett. A, 2003, 316(5):297-303.
[12] Cao Z L, Yang M. Probabilistic teleportation of unknown atomic state using W class states. Physica A, 2004, 337(l-2):132-140.
[13] Zheng S B. Scheme of rapproximate conditional teleportation of an unknown atomic state without the Bell-state measurement. Phys.Rev.A, 2004, 69(6):064302-064305.
[14] Ye L, Guo G C. Scheme for teleportation of an unknown atomic state without the Bell-state measurement. Phys. Rev. A, 2004, 70(5):054303-054306
[15] Hillery M, Buzek V, Berthiaume A. Quantum secret sharing. Phys. Rev. A, 1999, 59(3): 1829-1834.
[16] Bandyopadhyay S. Teleportation and secret sharing with pure entangled states. Phys.Rev. A, 2000, 62(l):012308-012311
[17] Gottesman D. Theory of quantum secret sharing. Phys. Rev. A, 2000, 61(4): 042311-042314
[18] Singh S K, Srikanth R. Generalized quantum secret sharing. Phys. Rev. A, 2005, 71(l):012328-012331
[19] Bostrom K, Felbinger T. Deterministic secure direct communication using entanglement. Phys. Rev. Lett., 2002, 89(18):187902-187905
[20] Deng F G, Long G L, Liu X S. A two-step quantum direct communication protocol using Einstein-podolsky-Rosen pair blocks. Phys. Rev. A, 2003, 68(4): 042317-042320
[21] Joo J, Park Y J. Quantum secure communication via a W state. J. Korean Phys. Soc, 2005, 46(4):765-768.
[22] Man Z X, Zhang Z J, Li Y. Deterministic secure direct communication by using swapping quantum entanglement and local unitary operations. Chin. Phys. Lett., 2005, 46(4): 765-768.
[23] Shor P W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 1995, 52(4):2493-2496.
[24] Zeng G H, Zhang W P. Identity verification in quantum key distribution. Phys. Rev. A, 2000, 61(2):022303-022306
[25] Cabello A. Quantum key distribution in the Holevo limit. Phys. Rev. Lett., 2000, 85(26):5635-5638.
[26] Cerf N J, Bourennane M, Karlsson A, et al. Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 2002, 88(12):127902-127905
[27] Han C, Xue P, Guo G C. A controlled quantum key distribution scheme with three-particle entanglement. Chin. Phys. Lett. 2003, 20(2): 183-185.
[28] Wang X B. Quantum key distribution with asymmetric channel noise. Phys. Rev. A, 2005, 71(5):052328-052331
[29] Lo H K, Ma X F, Chen K. Decoy state quantum key distribution. Phys. Rev. Lett., 2005, 94(23):230504-230507.
[30] Mattle K, Weinfurter H, Kwiat P G, et al. Dense coding in experimental quantum communication. Phys. Rev. Lett., 1996, 76(25):4656-4659.
[31] Bennett C H, Wisner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 1992, 69:2881-2884.
[32] Bennett C.H, et al. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett., 1993, 70:1895-1899.
[33] Feynman R. Simulating physics with computers. Int. J. Theor, Phys., 1982, 21:467-470.
[34] Feynman R. Quantum mechanical computer, Opt. News, 1985, 11:11; Quantum mechanical computers, Found. Phys, 1986, 16:507-510.
[35] 张永德．量子信息物理原理，北京：科学出版社，2006年．
[36] Shor P W. Algorithms for quantum computation: discrete logarithms and factoring, Proceeding, 35th Annual Symposium on Fundamentals of Computer Science, 1994.
[37] Grover L K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 1997, 79:325-328
[38] Barence A, Deutsch D, Ekert A, et al. Conditional quantum dynamics and logic gates. Phys. Rev. Lett., 1995, 74:4083-4086.
[39] Sleator T, Weinfurter H. Realizable universal quantum logic gates. Phys. Rev. Lett., 1995,74:4087-4090.
[40] Cirac J I, Zoller P. Quantum computation with cold trapped ions. Phys. Rev. Lett., 1995, 74:4091-4094.
[41] Steane A. The ion trap quantum information processor. Applied Physics B: Laser and Optics, 1997, 64:623-643.
[42] Warren W S. The usefulness of nmr quantum computing. Science, 1997, 277: 1688-1690.
[43] Gershenfeld N A, Chuang I L. Bulk spin-resonance quantum computation. Science, 1997,275:350-356.
[44] Jones J A, Vedral V. Geometric quantum computation using nuclear magnetic resonance. Nature, 2000,403:869-871.
[45] Loss D, Di Vincenzo D P. Quantum computation with quantum dots. Phys. Rev. A, 1998, 57:120-126.
[46] Piermarocchi C, Chen P, Sham L J, et al. Optical rkky interaction between charged semiconductor quantum dots. Phys. Rev. Lett., 2002, 89:167402-167405.
[47] Zheng S B, Guo G C. Efficient scheme for two-atom entanglement and quantum information processing in cavity QED [J]. Phys. Rev. Lett, 2000, 85:2392-2395.
[48] Y. Feng, S. Y. Zhang, M. S. Ying. Probabilistic cloning and deleting of quantum states. Phys. Rev. A, 2002, 65:4-7
[49] Zhang S Y, Ying M S. Set discrimination of quantum states, Phys. Rev. A, 2002, 65:6-9
[50] Sun X M, Zhang S Y, Feng Y, et al. Mathematical nature of and an lower bound for the success probability of umambiguous discrimination of quantum states. Phys. Rev. A, 2002, 65:4-7.
[51] Ying M S. Universal quantum copying machines: a necessary and sufficient condition. Phys. Let.A, 2002, 302:1-4.
[52] Bouwmeecter D, Pan J W, Mattle K, et al. Experimental quantum teleportation [J]. Nature, 1997, 390:575-577.
[53] Pan J W, Bouwmeecter D, Weinfurter H, et al. Experimental entanglement swapping: entangling photons that never inteareted. Phys. Rev. Lett, 1998, 80:3891-3894.
[54] Xiao Junjia, Su Xiaolong, Pan Qing, et al. Experimental demonstartion of unconditional entanglement swpaping for continuous variables, Phys. Rev. Lett. 2004, 93:250503-250506.
[55] Furusawa A, Sorensen J L, Braunstein S L, et al. Unconditional quantum teleportation [J]. Science, 1998,282:706-709.
[56] Vaidman L. Teleportation of quantum states [J]. Phys. Rev. A, 1994,49:1473-1476.
[57] Braunstein S L, Kimble H J. Teleportation of continuous quantum variables [J]. Phys. Rev. Lett, 1998, 80:869-872.
[58] Zukowshi M, et al. "Event-ready-detectors"Bell experiment via entanglement swapping [J]. Phys. Rev. Lett., 1993, 71:4287-4290.
[59] Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states [J]. Phys. Rev. Lett., 1992, 69:2881-2884.
[60] Ekert A K. Quantum cryptography based on Bell's theorm [J]. Phys. Rev. Lett., 1991, 67:661-663.
[61] Hagley E, et al. Generation of Einstein-Podolsky-Rosen pairs of atoms [J]. Phys. Rev. Lett., 1997,79:1-5.
[62] Rauschenbeutel A, Nogues G, Osnaghi S, et al. Step-by-step engineered mutliparticle entanglement. Science, 2000,288:2024-2028.
[63] Braunstein S L. Error correction for continuous quantum variables [J]. Phys. Rev. Lett., 1998, 80:4084-4087.
[64] Braunstein S L, Pati A K, eds. Quantum information with continuous variables. Kluwer Academic, 2003.
[65] Braunstein S L, Look P van. Quantum information with continuous variables. Rev. Mod. Phys., 2005, 77:513-577.
[66] Cerf N J, Grangier P. Detection of resonance space-charge wave peaks for holes and electrons in photorefractive crystals. J. Opt. Soc. Am. 2007, B24, 324-327.
[67] Meekhof D M, Monroe C, King B E, et al. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett., 1996, 76:1796-1799.
[68] Monroe C, Meekhor D M, King B E, et al. Resolvd-sideband Raman cooling of a bound atom to the 3D zero-point energy. Phys. Rev. Lett., 1996, 75:4011-4014.
[69] Bell J S, Physics, 1965, 1:195-198.
[70] 张永德等．量子信息论-物理原理和某些进展[M]．武汉：华中师范大学出版社，2002年，165-169．
[71] 李崇．量子通讯理论的矩阵表述．大连理工大学博士学位论文，2003年．
[72] 张永德．量子信息物理原理．科学出版社，2006年
[73] Plenio M B, Virmani S. Quant. Inf. Comput. 2007, 7:1
[74] 华中师范大学博士学位论文．连续变量纠缠及量子点输运性质的控制．柯莎莎．2008年．
[75] Peres A. Separability criterion for density matrices. Phys. Rev. Lett., 1996, 77:1413-1417.
[76] Horodecki M, Horodecki P, Horodecki R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 1996, 233:1-4.
[77] Simon R. Peres-Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 2000, 84:2726-2729.
[78] Duan Lu-Ming, Giedke G., Cirac J I, et al. Inseparability criterion for continuous variable systems. Phys. Rev. Lett., 2000, 84:2722-2725.
[79] Xia Yun-jie, Guo Guang-can. Squeezing and entanglement in continuous variable systems. Chin. Phys. Lett. 2004, 21:1877-1880.
[80] Shchukin E, Vogel W. Inseparability criteria for continuous bipartite quantum state. Phys. Rev. Lett, 2005, 95:230502-230505.
[81] Agarwal G S, Biswas A. Inseparability inequalities for higher order moments for bipartite systems. New Journal of Physics, 2005, 7:211.
[82] Hyllus P, Eisert J. Optimal entanglement witnesses for continuous-variable systems. New Journal of Physics, 2006, 8:51
[83] Hillery M, Zubairy M S. Entanglement conditions for two-mode states. Phys.Rev. Lett. 2006, 96:050503-050306.
[84] Jaynes E T, Commings F W. Proc. IEEE 51 No.l (Jan) 1963, 89.
[85] Bennett C H, Brassard G, Jozsa R. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels [J]. Phys. Rev. Lett, 1993, 70(13): 1865-1869.
[86] Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation [J]. Nature, 1997, 390:575-579.
[87] Shor P W. Scheme for reducing decoherence in quantum computer memory [J]. Phys. Rev. A, 1995, 52:2493-2496.
[88] Giovannetti V, Loyd S, Maccone L. Positioning and clock synchronization through entanglemen [J]. Phys. Rev. A, 2002, 65(2):022309-022317.
[89] Li G X, Allart K, Lenstra D. Entanglement between two atoms in an overdamped cavity injected with squeezed vaccum [J]. Phys. Rev. A, 2004,69:055802-055805.
[90] Zou X B, Pahlke K, Mathis W. Generation of an entangled four-photon W state [J]. Phys .Rev. A, 2002,67:044302-044305.
[91] Bourennane M, Karlsson A, Bjork G, et al. Quantum Key Distribution using multilevel encoding: Seacuriyt Analysis [J]. J. Phys.A, 2002, 64:012306-012309.
[92] Burss D, Macchiavello C. Optimal eavesdropping in Cryptography with three-dimensional quantum states [J]. Phys. Rev. Lett, 2002, 88:127901-127904.
[93] Cerf N J, Bourennane M, Karlsson A, et al. Security of quantum key distribution using d-level systems [J]. Phys. Rev. Lett, 2002, 88:127902-127905.
[94] Kaszlikowski D, Gnacinski P, Zukowski M, et al. Violations of local realism by two entangled qubits is stronger than for two qubits [J]. Phys. Rev. Lett., 2000, 85:4418-4421.
[95] Acin A, Durt T, Gisin N, et al. Quantum non-locality in two three-level systems [J]. Phys. Rev. A, 2002, 65:052325-052328.
[96] Chen J L, Kaszlikowski D, Kwek L C, et al. Searching a database under decoherence [J]. Phys. Rev. A, 2001, 64:052109-052112.
[97] Xiong H, Scully M O, Zubairy M S, Correlated spontaneous emission laser as an entanglement amplifer. Phys. Rev. Lett., 2005, 94, 023601-023604.
[98] Li F L, Xiong H, Zubairy M S. Coherence-induced entanglement. Phys. Rev. A, 2005, 72:010303-010306.
[99] Tan H T, Zhu S Y, Zubairy M S. Continuous-variable entanglement in a correlated spontaneous emission laser. Phys. Rev. A, 2005, 72:022305-022308
[100]Tesfa S. Entanglement amplification in a nondegenerate three-level cascade laser. Phys. Rev. A, 2006, 74:043816-043819.
[101]夏云杰．腔QED中加宽原子的自发辐射和量子纠缠态的研究．中国科技大学博士学位论文，2007年．
[102]Scully M O, Zubairy M S. Quantum Optics, Cambridge University Press, 1999, 146-q50.
[103]Ansari N A. Theory of a two-mode phase-sensitive amplifier. Phys. Rev. A, 1992, 46:1560-1564.
[104]Josse V, Dantan A, Bramati A, Pinard M, et al. Phys. Rev. Lett., 2004, 92:123601-123604.
[105]Guzman R, Retamal J C, Solano E, et al. Field squeezze operators in optical cavities with atomic ensembles. Phys. Rev. Lett., 2006, 96:010502-010505.
[106]Collet M J, Gardiner C W. Squeezing of intracavity and travelling-wave light fields produced in parametric amplification. Phys. Rev. A, 1984, 30:1386-1391.
[107]Holm D A, Sargent Ⅲ M. Quantum theory ofmultiwave mixing. Ⅷ. Squeezed states. Phys. Rev. A, 1987, 35:2150-2163.
[108] An S, Sargent M. Quantum theory of multiwave mixing. X. Two-photon three-level mode. Phys. Rev. A, 1989, 39:1841-1847.
[109]Bohm D. Quantum Theory [M]. New York: Prentice Hall, 1951, 614-619.
[110]Bohm D. A suggested interpretation of quantum theory in terms of "hidden variable" [J]. Phys. Rev., 1952,166-179.
[111]Aspect A, et al. Experimental test of Bell's inequalities using time-varying analyzers. Phys. Rev. Lett., 1982,49:1804-1807.
[112]Ansari N A, Gea-Banacloche J, Zubairy M S. Phase-sensitive amplification in a three-level atomic system. Phys. Rev. A, 1990, 41:5179-5186; Majeed M, Zubairy M S. Role of pump phase fluctuation in a two-photon phase-sensitive amplifier. Phys. Rev. A, 1995,52:2350-2360.
[113]Tan H T, Zhu S Y, Zubairy M S. Continuous-variable entanglement in a correlated spontaneous emission laser. Phys. Rev. A, 2005, 72:022305(8).
[114]Shchukin, Vogel. Inseparability criteria for continuous bipartite quantum states. Phys. Rev. Lett., 2005, 95:230502(4).
[115]Ansari N A. Violation of Bell's inequality in a driven three-level cascade atomic system. Phys. Rev. A, 1997, 55:1639-1646.
[116]Ansari N A, Zubairy M S. Violation of Cauchy-Schwarz and Bell's inequalities in four-wave mixing. Phys. Rev. A, 1988,38:2380-2385.
[117]Loss D, DiVincenzo D P. Quantum computation with quantum dots. Phys. Rev. A, 1998, 57:120-126; Makhlin Y, Sch(?)on G, Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys., 2001, 73:357-400.
[118]Hichri A, Jaziri S. Entanglement and Zeeman interaction in diluted magnetic semiconductor quantum dot. Physica B, 2004, 350:305-312; Plastina F, Fazio R, Palma G M. Macroscopic entanglement in Josephson nanocircuits. Phys. Rev. B, 2001, 64:113306(4); Ruskov R, Korotkov A N. Entanglement of solid-state qubits by measurement. Phys. Rev. B, 2005, 67:241305(4).
[119]Levine G, Muthukumar V N. Phys. Rev. B, 2004, 69:113203; Paternostro M, Falci G, Kim M, et al. Phys. Rev. B, 2004, 69:214502; Doucot B, Ioffe L B. New J. Phys., 2005,7:187.
[120]Bao J M, Bragasa A V, Furdynab J K, et al. Optical implement of entanglement multi-spin states in a CdTe quantum well. Solid State Commun. 2003,127:771-775.
[121]Gedik Z. Quantum entanglement and order parameter in a paired finite Fermi system. Solid State Commun. 2002,124:473-476; Gedik Z. Spin bath decoherence of quantum entanglement. Solid State Commun. 2006,138:82-85.
[122]Wang X B. Theorem for the beam-splitter entangler. Phys. Rev. A, 2002, 66(2): 024303(2).
[123]Kim M S, Son W, Buzek V, et al. Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement. Phys. Rev. A, 2002, 65(3):032323(7).
[124]Feng X L, Li R X, Xu Z Z. Beam splitter entangler for light fields. Phys. Rev. A, 2005, 71(3):032335(4).
[125]Haine S A, Olsen M K, Hope J J. Generating controllable atom-light entanglement with raman atom laser system. Phys. Rev. Lett., 2006,96(13): 133601(4).
[126]Silberfarv A, Deutsch Ivan H. Entanglement generated between a single atom and a laser pulse. Phys. Rev. A, 2004,69(4):042308(8).
[127]Duan L M. Entanglement many atomic ensembles through laser manipulation. Phys. Rev. Lett., 20026, 88(17): 170402(4).
[128]Ping YX, Zhang B, Cheng Z. Generation of entanglement via atomic coherence in a two-mode three-level cascade atomic system. Eur. Phys. J. D, 2007, 44:175-180; Ping Y X, Zhang B, Cheng Z. Theory of a two-mode entanglement amplifier. Phys. Lett. A, 2007, 366:596-599.
[129]Gordona A, Logoboyb N, Joss W. Magnon softening in metals at quantizing magnetic fields. Solid State Commun. 2004, 130: 131-135.
[130]Owens F J, Orosz J. Effect of nanosizing on lattice and magnon modes of hematite. Solid State Commun. 2006,138:95-98.
[131]Feng P. Self-squeezing states of magnons in an antiferromagnet. Eur. Phys. Lett., 2001, 54:688-692.
[132]Zhao J, Bragas A V, Lockwood D J, et al. Magnon squeezing in an antiferromagnet: Reducing the spin noise below the standard quantum limit. Phys. Rev. Lett. 2004, 93:107203(4).
[133]Zhao J, Bragas A V, Merlin R, et al. Magnon squeezing in antiferromagnetic MnF_(2) and FeF_(2). Phys. Rev. B, 2006,73:184434(11).
[134]Pratt J S. Qubit entanglement in multimagnon states. Phys. Rev. B, 2006, 73:184413(8).
[135]姜寿亭.铁磁性理论,北京:科学出版社,79-135.
[136] Callaway J. Quantum theory of the solid state. Academic Press, New York, 1976.
[137]Kittel C. Introduction to solid state physics. Wiley, New York, 1976.
[138]Haley S B, Erdos P. Standard-basis operator method in the Green's-function thechnique of many-body systems with an application to ferromagnetism. Phys. Rev. B, 1972,5:1106-1119.
[139]Biegala J, Ulner Z. Phys. B, 1983,50:45.
[140]Peng F. Crystal-field-modulated magnon squeezing states in a ferromagnet. Physica B, 2003,334:183-187.
[141] Yuen H P. Two-photon coherent states of the radiation field. Phys. Rev. A, 1976, 13(6): 2226-2243.
[142]Xia Y J, Guo G .C. Nonclassical properties of even and odd coherent states. Phys. Lett. A, 1989, 136(6):281-283.
[143]Pathak P K, Agarwal G S. Generation of a superposition of multiple mesoscopic states of radiation in a cavity. Phys. Rev. A, 2005, 71:043823(6).
[144]Aafarwal G S, Tara K. Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A, 1991,43:492-497.
[145]Zhang Z, Fan H Y. Properties of states generated by excitation on a squeezed vacuum state. Phys. Lett. A, 1992, 165:14-18.
[146]Lu H, Guo G C. Acta Phys. Sin., 1999, 48 1644(in Chinese)
[147]Chai C L. Two-mode nonclassical state via superpositions of two-mode coherent states. Phys. Rev. A, 1992, 46:7187-7191.
[148]Wang X G. Quantum teleportation of entangled coherent states. Phys. Rev. A, 2001, 64:022302(4); Van Enk S J, Hirota O. Entangled coherent states: Teleportation and decoherence. Phys. Rev. A, 2001, 64:022313(6).
[149]Peng J S, Li G X. Introduction to modern quantum optics, (World Scientific, Singapore). 1998.
[150]汪德新．量子力学，北京：科学出版社，2003年．
[151]Glauber R J. Coherent and incoherent states of the radiation field. Phys. Rev., 1963, 131:2766-2788.
[152]Slusher R E, Hollberg L W, Yurke B, et al. Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett., 1985, 55:2409-2412.
[153]Stoler D. Equivalence classes of minimum uncertainty packets. Phys. Rev., 1970, D1:3217-3220.
[154]许定国．多态叠加多模叠加光场等幕高次压缩特性研究．西安电子科技大学博士论文，2005年．
[155]Walls D F. Squeezed states of light [J]. Nature, 1983, 306(11):141-146.
[156]Loudon R, Knight P L. Squeezed light [J]. J. Mod. Opt., 1987, 34(6/7):709-759.
[157]Hong C K, L. Mandel. Generation of higher-order squeezing of quantum electromagnetic fields. Phys. Rev. A, 1985, 32(2):971-982.
[158]Hillery M. Amplitude-squared squeezing of the electromagnetie field [J]. Phys. Rev. A, 1987, 36(8):3796-3802.
[159]Hillery M. Sum and differenee squeezing of the eleetromagnetie field [J]. Phys. Rev. A, 1989, 40(6):3147-3155.
[160]Zhang Z M, Xu L, Chai J, et al. A new kind of higher-order squeezing of rediation field. Phys. Lett. A, 1990, 150(1):27-30.
[161]Bergou J A, Hillery M, Yu D. Minium uncertainty states for amplitude-squared squeezing: Hermite Polynomial states. Phys. Rev. A, 1991, 43(1):515-520.
[162]董传华．高阶压缩的另一种定义，光学学报，1996，16(11)：1543-1548．
[163]Kim M S, A. Oliveriva M, Knight P L. Photo number distribution for squeezed number states and squeezed thermal states [J]. Opt. Conunum., 1989, 72(1/2):99-103.
[164]Gerry C C. Correlated two-mode SU (1, 1) coherent states: non- classical properties [J]. J.Opt. Soe. Am. B, 1991, 8(3):685-690.
[165]彭垫墀，黄茂全等．双模光场压缩态的实验研究[J]．物理学报，1993，42(7)：1079-1085．
[166]Wodkiewize K, Eberly J H, Gerry C C. Coherent states squeezed fluctuation and the SU(2) and SU(1,1) groups in quantum optics applications [J]. J.OPt.Soe.Am. (B), 1982, 2(3): 485-486.
[167]Gerry C C. Application of SU (1, 1) coherent states to the interaction of squeezed light in a homonic oscillator [J]. Phys. Rev. A, 1987, 35(5):2146-2149.
[168]韩小卫，杨志勇等．第1种非对称两态叠加多模叠加态光场的奇次幂N次方Y压缩[J]．光子学报，2002，31(11)：1297-1280．
[169]杨志勇，孙忠禹等．第Ⅱ类三态叠加多模叠加态光场等幂次2m+1次方Y压缩[J]．光子学报，2002，3 1(7)：785-788．
[170]彭金生，李高翔．近代量子光学导论，北京：科学出版社，1996年．
[171]杨伯君著．量子光学基础，北京：北京邮电大学出版社，1996年．
[2] 郭光灿．量子信息引论．见：曾谨言，裴寿镛．99量子力学新进展(第一辑)．北京：北京大学出版社，2000年，249-285．
[3] Michael A, Nielsen, Issac L. Chuang, Quantum computation and quantum information, Cambridge University Press: Cambridge (2000).
[4] Schrodinger E. Die gegenw artige situation in der quantenme chanik [J]. Naturwissenschaften, 1935, 23:807.
[5] Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev, 1935, 47: 777-780.
[6] Bennett C H, Brassard G, Crepeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 1993, 70 (13):1895-1899.
[7] Zheng Y Z, Gu Y J, Guo G C. Teleportation of a three-particle entangled W state. Chin. Phys. 2002, 11 (6):537-542.
[8] Dai H Y, Chen P X, Li C Z. Probabilistic teleportation of an arbitrary two-particle state by two partial three-particle entangled W states. J. Opt. B: Quantum Semiclass. Opt., 2004, 6(1): 106-109.
[9] Zhou L, Kuang L M. Linear optical implementation for quantum teleportation of unknown two-qubit entangled states. Chin. Phys. Lett. 2004, 21 (11): 2101-2104.
[10] Guerra E S. Teleportation of atomic states via cavity quantum electrodynamics. Opt. Commun. 2004, 242(4-6):541-549.
[11] Yan F L, Wang D. Probabilistic and controlled teleportation of unknown quantum states. Phys. Lett. A, 2003, 316(5):297-303.
[12] Cao Z L, Yang M. Probabilistic teleportation of unknown atomic state using W class states. Physica A, 2004, 337(l-2):132-140.
[13] Zheng S B. Scheme of rapproximate conditional teleportation of an unknown atomic state without the Bell-state measurement. Phys.Rev.A, 2004, 69(6):064302-064305.
[14] Ye L, Guo G C. Scheme for teleportation of an unknown atomic state without the Bell-state measurement. Phys. Rev. A, 2004, 70(5):054303-054306
[15] Hillery M, Buzek V, Berthiaume A. Quantum secret sharing. Phys. Rev. A, 1999, 59(3): 1829-1834.
[16] Bandyopadhyay S. Teleportation and secret sharing with pure entangled states. Phys.Rev. A, 2000, 62(l):012308-012311
[17] Gottesman D. Theory of quantum secret sharing. Phys. Rev. A, 2000, 61(4): 042311-042314
[18] Singh S K, Srikanth R. Generalized quantum secret sharing. Phys. Rev. A, 2005, 71(l):012328-012331
[19] Bostrom K, Felbinger T. Deterministic secure direct communication using entanglement. Phys. Rev. Lett., 2002, 89(18):187902-187905
[20] Deng F G, Long G L, Liu X S. A two-step quantum direct communication protocol using Einstein-podolsky-Rosen pair blocks. Phys. Rev. A, 2003, 68(4): 042317-042320
[21] Joo J, Park Y J. Quantum secure communication via a W state. J. Korean Phys. Soc, 2005, 46(4):765-768.
[22] Man Z X, Zhang Z J, Li Y. Deterministic secure direct communication by using swapping quantum entanglement and local unitary operations. Chin. Phys. Lett., 2005, 46(4): 765-768.
[23] Shor P W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 1995, 52(4):2493-2496.
[24] Zeng G H, Zhang W P. Identity verification in quantum key distribution. Phys. Rev. A, 2000, 61(2):022303-022306
[25] Cabello A. Quantum key distribution in the Holevo limit. Phys. Rev. Lett., 2000, 85(26):5635-5638.
[26] Cerf N J, Bourennane M, Karlsson A, et al. Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 2002, 88(12):127902-127905
[27] Han C, Xue P, Guo G C. A controlled quantum key distribution scheme with three-particle entanglement. Chin. Phys. Lett. 2003, 20(2): 183-185.
[28] Wang X B. Quantum key distribution with asymmetric channel noise. Phys. Rev. A, 2005, 71(5):052328-052331
[29] Lo H K, Ma X F, Chen K. Decoy state quantum key distribution. Phys. Rev. Lett., 2005, 94(23):230504-230507.
[30] Mattle K, Weinfurter H, Kwiat P G, et al. Dense coding in experimental quantum communication. Phys. Rev. Lett., 1996, 76(25):4656-4659.
[31] Bennett C H, Wisner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 1992, 69:2881-2884.
[32] Bennett C.H, et al. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett., 1993, 70:1895-1899.
[33] Feynman R. Simulating physics with computers. Int. J. Theor, Phys., 1982, 21:467-470.
[34] Feynman R. Quantum mechanical computer, Opt. News, 1985, 11:11; Quantum mechanical computers, Found. Phys, 1986, 16:507-510.
[35] 张永德．量子信息物理原理，北京：科学出版社，2006年．
[36] Shor P W. Algorithms for quantum computation: discrete logarithms and factoring, Proceeding, 35th Annual Symposium on Fundamentals of Computer Science, 1994.
[37] Grover L K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 1997, 79:325-328
[38] Barence A, Deutsch D, Ekert A, et al. Conditional quantum dynamics and logic gates. Phys. Rev. Lett., 1995, 74:4083-4086.
[39] Sleator T, Weinfurter H. Realizable universal quantum logic gates. Phys. Rev. Lett., 1995,74:4087-4090.
[40] Cirac J I, Zoller P. Quantum computation with cold trapped ions. Phys. Rev. Lett., 1995, 74:4091-4094.
[41] Steane A. The ion trap quantum information processor. Applied Physics B: Laser and Optics, 1997, 64:623-643.
[42] Warren W S. The usefulness of nmr quantum computing. Science, 1997, 277: 1688-1690.
[43] Gershenfeld N A, Chuang I L. Bulk spin-resonance quantum computation. Science, 1997,275:350-356.
[44] Jones J A, Vedral V. Geometric quantum computation using nuclear magnetic resonance. Nature, 2000,403:869-871.
[45] Loss D, Di Vincenzo D P. Quantum computation with quantum dots. Phys. Rev. A, 1998, 57:120-126.
[46] Piermarocchi C, Chen P, Sham L J, et al. Optical rkky interaction between charged semiconductor quantum dots. Phys. Rev. Lett., 2002, 89:167402-167405.
[47] Zheng S B, Guo G C. Efficient scheme for two-atom entanglement and quantum information processing in cavity QED [J]. Phys. Rev. Lett, 2000, 85:2392-2395.
[48] Y. Feng, S. Y. Zhang, M. S. Ying. Probabilistic cloning and deleting of quantum states. Phys. Rev. A, 2002, 65:4-7
[49] Zhang S Y, Ying M S. Set discrimination of quantum states, Phys. Rev. A, 2002, 65:6-9
[50] Sun X M, Zhang S Y, Feng Y, et al. Mathematical nature of and an lower bound for the success probability of umambiguous discrimination of quantum states. Phys. Rev. A, 2002, 65:4-7.
[51] Ying M S. Universal quantum copying machines: a necessary and sufficient condition. Phys. Let.A, 2002, 302:1-4.
[52] Bouwmeecter D, Pan J W, Mattle K, et al. Experimental quantum teleportation [J]. Nature, 1997, 390:575-577.
[53] Pan J W, Bouwmeecter D, Weinfurter H, et al. Experimental entanglement swapping: entangling photons that never inteareted. Phys. Rev. Lett, 1998, 80:3891-3894.
[54] Xiao Junjia, Su Xiaolong, Pan Qing, et al. Experimental demonstartion of unconditional entanglement swpaping for continuous variables, Phys. Rev. Lett. 2004, 93:250503-250506.
[55] Furusawa A, Sorensen J L, Braunstein S L, et al. Unconditional quantum teleportation [J]. Science, 1998,282:706-709.
[56] Vaidman L. Teleportation of quantum states [J]. Phys. Rev. A, 1994,49:1473-1476.
[57] Braunstein S L, Kimble H J. Teleportation of continuous quantum variables [J]. Phys. Rev. Lett, 1998, 80:869-872.
[58] Zukowshi M, et al. "Event-ready-detectors"Bell experiment via entanglement swapping [J]. Phys. Rev. Lett., 1993, 71:4287-4290.
[59] Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states [J]. Phys. Rev. Lett., 1992, 69:2881-2884.
[60] Ekert A K. Quantum cryptography based on Bell's theorm [J]. Phys. Rev. Lett., 1991, 67:661-663.
[61] Hagley E, et al. Generation of Einstein-Podolsky-Rosen pairs of atoms [J]. Phys. Rev. Lett., 1997,79:1-5.
[62] Rauschenbeutel A, Nogues G, Osnaghi S, et al. Step-by-step engineered mutliparticle entanglement. Science, 2000,288:2024-2028.
[63] Braunstein S L. Error correction for continuous quantum variables [J]. Phys. Rev. Lett., 1998, 80:4084-4087.
[64] Braunstein S L, Pati A K, eds. Quantum information with continuous variables. Kluwer Academic, 2003.
[65] Braunstein S L, Look P van. Quantum information with continuous variables. Rev. Mod. Phys., 2005, 77:513-577.
[66] Cerf N J, Grangier P. Detection of resonance space-charge wave peaks for holes and electrons in photorefractive crystals. J. Opt. Soc. Am. 2007, B24, 324-327.
[67] Meekhof D M, Monroe C, King B E, et al. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett., 1996, 76:1796-1799.
[68] Monroe C, Meekhor D M, King B E, et al. Resolvd-sideband Raman cooling of a bound atom to the 3D zero-point energy. Phys. Rev. Lett., 1996, 75:4011-4014.
[69] Bell J S, Physics, 1965, 1:195-198.
[70] 张永德等．量子信息论-物理原理和某些进展[M]．武汉：华中师范大学出版社，2002年，165-169．
[71] 李崇．量子通讯理论的矩阵表述．大连理工大学博士学位论文，2003年．
[72] 张永德．量子信息物理原理．科学出版社，2006年
[73] Plenio M B, Virmani S. Quant. Inf. Comput. 2007, 7:1
[74] 华中师范大学博士学位论文．连续变量纠缠及量子点输运性质的控制．柯莎莎．2008年．
[75] Peres A. Separability criterion for density matrices. Phys. Rev. Lett., 1996, 77:1413-1417.
[76] Horodecki M, Horodecki P, Horodecki R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 1996, 233:1-4.
[77] Simon R. Peres-Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 2000, 84:2726-2729.
[78] Duan Lu-Ming, Giedke G., Cirac J I, et al. Inseparability criterion for continuous variable systems. Phys. Rev. Lett., 2000, 84:2722-2725.
[79] Xia Yun-jie, Guo Guang-can. Squeezing and entanglement in continuous variable systems. Chin. Phys. Lett. 2004, 21:1877-1880.
[80] Shchukin E, Vogel W. Inseparability criteria for continuous bipartite quantum state. Phys. Rev. Lett, 2005, 95:230502-230505.
[81] Agarwal G S, Biswas A. Inseparability inequalities for higher order moments for bipartite systems. New Journal of Physics, 2005, 7:211.
[82] Hyllus P, Eisert J. Optimal entanglement witnesses for continuous-variable systems. New Journal of Physics, 2006, 8:51
[83] Hillery M, Zubairy M S. Entanglement conditions for two-mode states. Phys.Rev. Lett. 2006, 96:050503-050306.
[84] Jaynes E T, Commings F W. Proc. IEEE 51 No.l (Jan) 1963, 89.
[85] Bennett C H, Brassard G, Jozsa R. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels [J]. Phys. Rev. Lett, 1993, 70(13): 1865-1869.
[86] Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation [J]. Nature, 1997, 390:575-579.
[87] Shor P W. Scheme for reducing decoherence in quantum computer memory [J]. Phys. Rev. A, 1995, 52:2493-2496.
[88] Giovannetti V, Loyd S, Maccone L. Positioning and clock synchronization through entanglemen [J]. Phys. Rev. A, 2002, 65(2):022309-022317.
[89] Li G X, Allart K, Lenstra D. Entanglement between two atoms in an overdamped cavity injected with squeezed vaccum [J]. Phys. Rev. A, 2004,69:055802-055805.
[90] Zou X B, Pahlke K, Mathis W. Generation of an entangled four-photon W state [J]. Phys .Rev. A, 2002,67:044302-044305.
[91] Bourennane M, Karlsson A, Bjork G, et al. Quantum Key Distribution using multilevel encoding: Seacuriyt Analysis [J]. J. Phys.A, 2002, 64:012306-012309.
[92] Burss D, Macchiavello C. Optimal eavesdropping in Cryptography with three-dimensional quantum states [J]. Phys. Rev. Lett, 2002, 88:127901-127904.
[93] Cerf N J, Bourennane M, Karlsson A, et al. Security of quantum key distribution using d-level systems [J]. Phys. Rev. Lett, 2002, 88:127902-127905.
[94] Kaszlikowski D, Gnacinski P, Zukowski M, et al. Violations of local realism by two entangled qubits is stronger than for two qubits [J]. Phys. Rev. Lett., 2000, 85:4418-4421.
[95] Acin A, Durt T, Gisin N, et al. Quantum non-locality in two three-level systems [J]. Phys. Rev. A, 2002, 65:052325-052328.
[96] Chen J L, Kaszlikowski D, Kwek L C, et al. Searching a database under decoherence [J]. Phys. Rev. A, 2001, 64:052109-052112.
[97] Xiong H, Scully M O, Zubairy M S, Correlated spontaneous emission laser as an entanglement amplifer. Phys. Rev. Lett., 2005, 94, 023601-023604.
[98] Li F L, Xiong H, Zubairy M S. Coherence-induced entanglement. Phys. Rev. A, 2005, 72:010303-010306.
[99] Tan H T, Zhu S Y, Zubairy M S. Continuous-variable entanglement in a correlated spontaneous emission laser. Phys. Rev. A, 2005, 72:022305-022308
[100]Tesfa S. Entanglement amplification in a nondegenerate three-level cascade laser. Phys. Rev. A, 2006, 74:043816-043819.
[101]夏云杰．腔QED中加宽原子的自发辐射和量子纠缠态的研究．中国科技大学博士学位论文，2007年．
[102]Scully M O, Zubairy M S. Quantum Optics, Cambridge University Press, 1999, 146-q50.
[103]Ansari N A. Theory of a two-mode phase-sensitive amplifier. Phys. Rev. A, 1992, 46:1560-1564.
[104]Josse V, Dantan A, Bramati A, Pinard M, et al. Phys. Rev. Lett., 2004, 92:123601-123604.
[105]Guzman R, Retamal J C, Solano E, et al. Field squeezze operators in optical cavities with atomic ensembles. Phys. Rev. Lett., 2006, 96:010502-010505.
[106]Collet M J, Gardiner C W. Squeezing of intracavity and travelling-wave light fields produced in parametric amplification. Phys. Rev. A, 1984, 30:1386-1391.
[107]Holm D A, Sargent Ⅲ M. Quantum theory ofmultiwave mixing. Ⅷ. Squeezed states. Phys. Rev. A, 1987, 35:2150-2163.
[108] An S, Sargent M. Quantum theory of multiwave mixing. X. Two-photon three-level mode. Phys. Rev. A, 1989, 39:1841-1847.
[109]Bohm D. Quantum Theory [M]. New York: Prentice Hall, 1951, 614-619.
[110]Bohm D. A suggested interpretation of quantum theory in terms of "hidden variable" [J]. Phys. Rev., 1952,166-179.
[111]Aspect A, et al. Experimental test of Bell's inequalities using time-varying analyzers. Phys. Rev. Lett., 1982,49:1804-1807.
[112]Ansari N A, Gea-Banacloche J, Zubairy M S. Phase-sensitive amplification in a three-level atomic system. Phys. Rev. A, 1990, 41:5179-5186; Majeed M, Zubairy M S. Role of pump phase fluctuation in a two-photon phase-sensitive amplifier. Phys. Rev. A, 1995,52:2350-2360.
[113]Tan H T, Zhu S Y, Zubairy M S. Continuous-variable entanglement in a correlated spontaneous emission laser. Phys. Rev. A, 2005, 72:022305(8).
[114]Shchukin, Vogel. Inseparability criteria for continuous bipartite quantum states. Phys. Rev. Lett., 2005, 95:230502(4).
[115]Ansari N A. Violation of Bell's inequality in a driven three-level cascade atomic system. Phys. Rev. A, 1997, 55:1639-1646.
[116]Ansari N A, Zubairy M S. Violation of Cauchy-Schwarz and Bell's inequalities in four-wave mixing. Phys. Rev. A, 1988,38:2380-2385.
[117]Loss D, DiVincenzo D P. Quantum computation with quantum dots. Phys. Rev. A, 1998, 57:120-126; Makhlin Y, Sch(?)on G, Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys., 2001, 73:357-400.
[118]Hichri A, Jaziri S. Entanglement and Zeeman interaction in diluted magnetic semiconductor quantum dot. Physica B, 2004, 350:305-312; Plastina F, Fazio R, Palma G M. Macroscopic entanglement in Josephson nanocircuits. Phys. Rev. B, 2001, 64:113306(4); Ruskov R, Korotkov A N. Entanglement of solid-state qubits by measurement. Phys. Rev. B, 2005, 67:241305(4).
[119]Levine G, Muthukumar V N. Phys. Rev. B, 2004, 69:113203; Paternostro M, Falci G, Kim M, et al. Phys. Rev. B, 2004, 69:214502; Doucot B, Ioffe L B. New J. Phys., 2005,7:187.
[120]Bao J M, Bragasa A V, Furdynab J K, et al. Optical implement of entanglement multi-spin states in a CdTe quantum well. Solid State Commun. 2003,127:771-775.
[121]Gedik Z. Quantum entanglement and order parameter in a paired finite Fermi system. Solid State Commun. 2002,124:473-476; Gedik Z. Spin bath decoherence of quantum entanglement. Solid State Commun. 2006,138:82-85.
[122]Wang X B. Theorem for the beam-splitter entangler. Phys. Rev. A, 2002, 66(2): 024303(2).
[123]Kim M S, Son W, Buzek V, et al. Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement. Phys. Rev. A, 2002, 65(3):032323(7).
[124]Feng X L, Li R X, Xu Z Z. Beam splitter entangler for light fields. Phys. Rev. A, 2005, 71(3):032335(4).
[125]Haine S A, Olsen M K, Hope J J. Generating controllable atom-light entanglement with raman atom laser system. Phys. Rev. Lett., 2006,96(13): 133601(4).
[126]Silberfarv A, Deutsch Ivan H. Entanglement generated between a single atom and a laser pulse. Phys. Rev. A, 2004,69(4):042308(8).
[127]Duan L M. Entanglement many atomic ensembles through laser manipulation. Phys. Rev. Lett., 20026, 88(17): 170402(4).
[128]Ping YX, Zhang B, Cheng Z. Generation of entanglement via atomic coherence in a two-mode three-level cascade atomic system. Eur. Phys. J. D, 2007, 44:175-180; Ping Y X, Zhang B, Cheng Z. Theory of a two-mode entanglement amplifier. Phys. Lett. A, 2007, 366:596-599.
[129]Gordona A, Logoboyb N, Joss W. Magnon softening in metals at quantizing magnetic fields. Solid State Commun. 2004, 130: 131-135.
[130]Owens F J, Orosz J. Effect of nanosizing on lattice and magnon modes of hematite. Solid State Commun. 2006,138:95-98.
[131]Feng P. Self-squeezing states of magnons in an antiferromagnet. Eur. Phys. Lett., 2001, 54:688-692.
[132]Zhao J, Bragas A V, Lockwood D J, et al. Magnon squeezing in an antiferromagnet: Reducing the spin noise below the standard quantum limit. Phys. Rev. Lett. 2004, 93:107203(4).
[133]Zhao J, Bragas A V, Merlin R, et al. Magnon squeezing in antiferromagnetic MnF_(2) and FeF_(2). Phys. Rev. B, 2006,73:184434(11).
[134]Pratt J S. Qubit entanglement in multimagnon states. Phys. Rev. B, 2006, 73:184413(8).
[135]姜寿亭.铁磁性理论,北京:科学出版社,79-135.
[136] Callaway J. Quantum theory of the solid state. Academic Press, New York, 1976.
[137]Kittel C. Introduction to solid state physics. Wiley, New York, 1976.
[138]Haley S B, Erdos P. Standard-basis operator method in the Green's-function thechnique of many-body systems with an application to ferromagnetism. Phys. Rev. B, 1972,5:1106-1119.
[139]Biegala J, Ulner Z. Phys. B, 1983,50:45.
[140]Peng F. Crystal-field-modulated magnon squeezing states in a ferromagnet. Physica B, 2003,334:183-187.
[141] Yuen H P. Two-photon coherent states of the radiation field. Phys. Rev. A, 1976, 13(6): 2226-2243.
[142]Xia Y J, Guo G .C. Nonclassical properties of even and odd coherent states. Phys. Lett. A, 1989, 136(6):281-283.
[143]Pathak P K, Agarwal G S. Generation of a superposition of multiple mesoscopic states of radiation in a cavity. Phys. Rev. A, 2005, 71:043823(6).
[144]Aafarwal G S, Tara K. Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A, 1991,43:492-497.
[145]Zhang Z, Fan H Y. Properties of states generated by excitation on a squeezed vacuum state. Phys. Lett. A, 1992, 165:14-18.
[146]Lu H, Guo G C. Acta Phys. Sin., 1999, 48 1644(in Chinese)
[147]Chai C L. Two-mode nonclassical state via superpositions of two-mode coherent states. Phys. Rev. A, 1992, 46:7187-7191.
[148]Wang X G. Quantum teleportation of entangled coherent states. Phys. Rev. A, 2001, 64:022302(4); Van Enk S J, Hirota O. Entangled coherent states: Teleportation and decoherence. Phys. Rev. A, 2001, 64:022313(6).
[149]Peng J S, Li G X. Introduction to modern quantum optics, (World Scientific, Singapore). 1998.
[150]汪德新．量子力学，北京：科学出版社，2003年．
[151]Glauber R J. Coherent and incoherent states of the radiation field. Phys. Rev., 1963, 131:2766-2788.
[152]Slusher R E, Hollberg L W, Yurke B, et al. Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett., 1985, 55:2409-2412.
[153]Stoler D. Equivalence classes of minimum uncertainty packets. Phys. Rev., 1970, D1:3217-3220.
[154]许定国．多态叠加多模叠加光场等幕高次压缩特性研究．西安电子科技大学博士论文，2005年．
[155]Walls D F. Squeezed states of light [J]. Nature, 1983, 306(11):141-146.
[156]Loudon R, Knight P L. Squeezed light [J]. J. Mod. Opt., 1987, 34(6/7):709-759.
[157]Hong C K, L. Mandel. Generation of higher-order squeezing of quantum electromagnetic fields. Phys. Rev. A, 1985, 32(2):971-982.
[158]Hillery M. Amplitude-squared squeezing of the electromagnetie field [J]. Phys. Rev. A, 1987, 36(8):3796-3802.
[159]Hillery M. Sum and differenee squeezing of the eleetromagnetie field [J]. Phys. Rev. A, 1989, 40(6):3147-3155.
[160]Zhang Z M, Xu L, Chai J, et al. A new kind of higher-order squeezing of rediation field. Phys. Lett. A, 1990, 150(1):27-30.
[161]Bergou J A, Hillery M, Yu D. Minium uncertainty states for amplitude-squared squeezing: Hermite Polynomial states. Phys. Rev. A, 1991, 43(1):515-520.
[162]董传华．高阶压缩的另一种定义，光学学报，1996，16(11)：1543-1548．
[163]Kim M S, A. Oliveriva M, Knight P L. Photo number distribution for squeezed number states and squeezed thermal states [J]. Opt. Conunum., 1989, 72(1/2):99-103.
[164]Gerry C C. Correlated two-mode SU (1, 1) coherent states: non- classical properties [J]. J.Opt. Soe. Am. B, 1991, 8(3):685-690.
[165]彭垫墀，黄茂全等．双模光场压缩态的实验研究[J]．物理学报，1993，42(7)：1079-1085．
[166]Wodkiewize K, Eberly J H, Gerry C C. Coherent states squeezed fluctuation and the SU(2) and SU(1,1) groups in quantum optics applications [J]. J.OPt.Soe.Am. (B), 1982, 2(3): 485-486.
[167]Gerry C C. Application of SU (1, 1) coherent states to the interaction of squeezed light in a homonic oscillator [J]. Phys. Rev. A, 1987, 35(5):2146-2149.
[168]韩小卫，杨志勇等．第1种非对称两态叠加多模叠加态光场的奇次幂N次方Y压缩[J]．光子学报，2002，31(11)：1297-1280．
[169]杨志勇，孙忠禹等．第Ⅱ类三态叠加多模叠加态光场等幂次2m+1次方Y压缩[J]．光子学报，2002，3 1(7)：785-788．
[170]彭金生，李高翔．近代量子光学导论，北京：科学出版社，1996年．
[171]杨伯君著．量子光学基础，北京：北京邮电大学出版社，1996年．