利用原子系综产生压缩及纠缠光的研究
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摘要
量子纠缠态由于具有便捷、有效的操控性,使得其在量子信息领域发挥着不可或缺的作用。相应的研究亦取得了实验上的应用,诸如量子计算网络,逻辑门,密集编码,隐形传态等等。实现纠缠有许多方式,例如利用非简并的参数振荡,波混频作用,关联发射激光,克尔效应,原子相干等。随着纠缠研究的深入,多模纠缠也在理论上取得了发展,从三模纠缠、四模纠缠到集合模纠缠。另一方面,双模及多模压缩与双模及多模纠缠有着密切的关联。当压缩参数足够大时,我们能获得Einstein-Podolsky-Rosen (EPR)(?)(?)缠态。近来,人们通过光与原子系综的相互作用系统来获得双模压缩,也就是,在光腔中放置原子系综,让量子场与其耦合,原子系综可看作原子库。与此同时,探索此系统在连续变量量子计算网络中的实践和应用。本文中,我们主要研究多模光场与原子系综相互作用的物理机制,并由此提出新的方案来获得多模压缩态,进而得到GHZ和cluster纠缠态。论文里创新工作有以下几点：
1.我们描述了受经典场驱动的原子系综与一对腔场的近共振相互作用,在一定条件下形成参数转换。我们发现,此时计算出的双线性哈密顿量,不再依赖于原子翻转算符,而是与修饰态之间的布居差成正比。如果参数的选择合适,与色散情况相比,近共振条件下所获得的参数相互作用将被加强到至少两个量级。尽管在腔场中存在自发辐射,但在腔场形成的一对集合模的起伏中仍会出现相消干涉。当腔衰减率远远大于色散情况下的腔衰减率时,参数转换和相消干涉两个因素将使得输出场产生理想的压缩和EPR纠缠态。这个物理机制能被用于多能级原子系统,并且在基于腔量子电动力学获得光压缩及纠缠态的实验中具有优势。
2.以前的研究表明,通过二能级原子系综的近共振相互作用,能产生双模纠缠光。其物理机制在于,介质与经典场作用后使得两个新的光子进入腔场。现在我们将这个机制推广到三个独立的原子系综体系,通过四个非简并光场在三个原子系综之间建立级联型相互作用。计算分析的结果表明,本方案能产生连续变量的四模cluster态和GHZ态纠缠光。这个方案对于产生多体纠缠的优势在于,近共振条件下获得的耦合强度要远远大于通过远离共振条件下的参数转换从而获得的耦合强度。
3.我们描述了利用多模腔场和原子库相互作用下相应拉曼通道中存在的效应,得到量子关联。分析显示,在多模场和原子系综的拉曼相互作用中,同时存在量子拍和四波混频过程。这两种物理机制相结合,能够使辐射光子成对地进入包含原子库的多模腔场。以四模场为例,我们提出一个方案,此方案在稳态时能产生四模压缩态,进而获得GHZ纠缠态,以及线形和方形的cluster纠缠态。这个系统不需要对原子态及腔模进行初始的制备,同时,此系统能有效克服原子自发衰减。
Entanglement play a vital role for quantum information because of its convenient and efficient operation in quantum processing. The corresponding researches has also been experimentally applied such as quantum communication network, logical gate, dense coding, and telecloning. There are various methods to achieve entanglement such as utilizing optical nondegenerate parametric oscillation, wave-mixing interaction, correlated emission laser, Kerr nonlinearity, atomic coherence effects and so on. Along with the development of the entanglement research, multimode entangled states of light have been theoretically proposed from tripartite, quadripatite to collective fields. On the other hand, two-or multimode squeezing are closely related to the two-mode and multimode entanglement. When the squeezing parameter is large one has Einstein-Podolsky-Rosen (EPR) entanglement. Recently, people use light interactions with atomic ensembles to achieve multimode squeezed and entangled states, i.e., an optical system on the basis of atomic ensemble couples to quantum light. A great deal of interest has been paid to the practical applications of atomic-field systems to quantum communication networks (QCNs). In this paper we have studied the interactions of multiple cavity fields with atomic ensembles and propose same new schemes for obtain multimode squeezed state, then Greenberger-Horne-Zeilinger (GHZ) and cluster entangled states. The main initiative results are presented as follows;
1. Parametric interaction of a pair of cavity fields in a near-resonantly driven atomic system is described by a bilinear Hamiltonian that decouples from atomic flip operators and is proportional to the population difference between dressed states. For proper choice of parameters, the parametric interaction is enhanced by at least two orders compared to the dispersively dressed cases. Although spontaneous emission is fed into the cavity fields, destructive interference occurs in the fluctuations of a pair of collective modes. As a result of the two factors, perfect squeezing and Einstein-Podolsky-Rosen entanglement in the output occur when the cavity relaxation rates are much larger than in the dispersive case. The mechanism is applicable to a great variety of multilevel systems and has experimental advantage in the cavity QED generation of squeezed and entangled states of light.
2. It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The respon- sible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nongenerate fields. It is shown that quadripartite cluster and Greenberger-Horne-Zeilinger entangled states happens for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance based parametric processes.
3. We describe the effects of Raman interactions on quantum correlations of the multimode optical fields. It is shown that both quantum beats and four-wave mixing processess exist in the Raman interactions of the multimode fields with atomic reservoirs. These two mechanisms combine to lead to emission in pairs into multiple cavity modes. Exemplify four cavity fields, we find that the four-mode squeezed state can be created at steady state. From this we can obtain the Greenberger-Horne-Zeilinger entangled state, and the linear and square cluster entangled states. This scheme does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay because of the absence of excitation.
1.我们描述了受经典场驱动的原子系综与一对腔场的近共振相互作用,在一定条件下形成参数转换。我们发现,此时计算出的双线性哈密顿量,不再依赖于原子翻转算符,而是与修饰态之间的布居差成正比。如果参数的选择合适,与色散情况相比,近共振条件下所获得的参数相互作用将被加强到至少两个量级。尽管在腔场中存在自发辐射,但在腔场形成的一对集合模的起伏中仍会出现相消干涉。当腔衰减率远远大于色散情况下的腔衰减率时,参数转换和相消干涉两个因素将使得输出场产生理想的压缩和EPR纠缠态。这个物理机制能被用于多能级原子系统,并且在基于腔量子电动力学获得光压缩及纠缠态的实验中具有优势。
2.以前的研究表明,通过二能级原子系综的近共振相互作用,能产生双模纠缠光。其物理机制在于,介质与经典场作用后使得两个新的光子进入腔场。现在我们将这个机制推广到三个独立的原子系综体系,通过四个非简并光场在三个原子系综之间建立级联型相互作用。计算分析的结果表明,本方案能产生连续变量的四模cluster态和GHZ态纠缠光。这个方案对于产生多体纠缠的优势在于,近共振条件下获得的耦合强度要远远大于通过远离共振条件下的参数转换从而获得的耦合强度。
3.我们描述了利用多模腔场和原子库相互作用下相应拉曼通道中存在的效应,得到量子关联。分析显示,在多模场和原子系综的拉曼相互作用中,同时存在量子拍和四波混频过程。这两种物理机制相结合,能够使辐射光子成对地进入包含原子库的多模腔场。以四模场为例,我们提出一个方案,此方案在稳态时能产生四模压缩态,进而获得GHZ纠缠态,以及线形和方形的cluster纠缠态。这个系统不需要对原子态及腔模进行初始的制备,同时,此系统能有效克服原子自发衰减。
Entanglement play a vital role for quantum information because of its convenient and efficient operation in quantum processing. The corresponding researches has also been experimentally applied such as quantum communication network, logical gate, dense coding, and telecloning. There are various methods to achieve entanglement such as utilizing optical nondegenerate parametric oscillation, wave-mixing interaction, correlated emission laser, Kerr nonlinearity, atomic coherence effects and so on. Along with the development of the entanglement research, multimode entangled states of light have been theoretically proposed from tripartite, quadripatite to collective fields. On the other hand, two-or multimode squeezing are closely related to the two-mode and multimode entanglement. When the squeezing parameter is large one has Einstein-Podolsky-Rosen (EPR) entanglement. Recently, people use light interactions with atomic ensembles to achieve multimode squeezed and entangled states, i.e., an optical system on the basis of atomic ensemble couples to quantum light. A great deal of interest has been paid to the practical applications of atomic-field systems to quantum communication networks (QCNs). In this paper we have studied the interactions of multiple cavity fields with atomic ensembles and propose same new schemes for obtain multimode squeezed state, then Greenberger-Horne-Zeilinger (GHZ) and cluster entangled states. The main initiative results are presented as follows;
1. Parametric interaction of a pair of cavity fields in a near-resonantly driven atomic system is described by a bilinear Hamiltonian that decouples from atomic flip operators and is proportional to the population difference between dressed states. For proper choice of parameters, the parametric interaction is enhanced by at least two orders compared to the dispersively dressed cases. Although spontaneous emission is fed into the cavity fields, destructive interference occurs in the fluctuations of a pair of collective modes. As a result of the two factors, perfect squeezing and Einstein-Podolsky-Rosen entanglement in the output occur when the cavity relaxation rates are much larger than in the dispersive case. The mechanism is applicable to a great variety of multilevel systems and has experimental advantage in the cavity QED generation of squeezed and entangled states of light.
2. It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The respon- sible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nongenerate fields. It is shown that quadripartite cluster and Greenberger-Horne-Zeilinger entangled states happens for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance based parametric processes.
3. We describe the effects of Raman interactions on quantum correlations of the multimode optical fields. It is shown that both quantum beats and four-wave mixing processess exist in the Raman interactions of the multimode fields with atomic reservoirs. These two mechanisms combine to lead to emission in pairs into multiple cavity modes. Exemplify four cavity fields, we find that the four-mode squeezed state can be created at steady state. From this we can obtain the Greenberger-Horne-Zeilinger entangled state, and the linear and square cluster entangled states. This scheme does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay because of the absence of excitation.
引文
[1]von Neumann J 1932 Mathematische Grundlagen der Quantenmechanic (Berlin:Springer)
[2]Einstein A, Podolsky B and Rosen N 1935 Phys. Rev.47 777
[3]Schrodinger E 1935 Naturwiss 23 807
[4]Bell J S 1964 Physics 1 195
[5]Gisin N 1991 Phys. Lett. A 154 201
[6]Popescu S and Rohrlich D 1992 Phys. Lett. A 166 293
[7]Kocher C A and Commins E D 1967 Phys. Rev. Lett.18 575
[8]Freedman S J and Clauser J F 1972 Phys. Rev. Lett.28 938
[9]Aspect A, Dalibard J and Roger G 1982 Phys. Rev. Lett.49 1804
[10]Aspect A, Grangier P and Roger G 1981 Phys. Rev. Lett.47 460
[11]Ou Z Y and Mandel L 1988 Phys. Rev. Lett.61 50
[12]Kwiat P G, Mattle K, Weinfurter H et al 1995 Phys. Rev. Lett.75 4337
[13]Tittel W, Brendel J, Zbinden H and Gisin N 1998 Phys. Rev. Lett.81 3563
[14]Tittel W, Brendel J, Gisin N and Zbinden H 1999 Phys. Rev. A 59 4150
[15]Weihs G, Jennewein T, Simon C et al 1998 Phys. Rev. Lett.81 5039
[16]Rowe M A et al 2001 Nature (London) 409 791
[17]Hasegawa Y, Loidl R, Badurek G et al 2004 J. Opt. B:Quantum Semiclassical Opt. 6S7
[18]Bovino F A, Giardina M, Svozil K and Vedral V 2006 e-print arXiv:quant-ph 0603167
[19]Ursin R et al 2007 Nat. Phys.3 481
[20]Gonta D, Pritzsche S and Radtke T 2003 Phys. Rev. A 77 062312
[21]Morrison S and Parkins A S 2006 Phys. Rev. A 74043810
[22]Shu J, Zou X B, Xiao Y F and Guo G C 2006 Phys. Rev. A 74 044301
[23]Zhang X L, Guo K L and Feng M 2006 Phys. Rev. A 74 024303
[24]Zhou D L, Sun B, Sun C P and You L 2005 Phys. Rev. A 72 040302
[25]Zou X B and Mathis W 2004 Phys. Rev. A 70 035802
[26]Li G X and Wu S P 2005 Phys. Rev. A 72 064304
[27]Haljan P C, Lee P J, Brickman K A et al 2005 Phys. Rev. A 72 062316
[28]Yang W X, Zhan Z M and Li J H 2005 Phys. Rev. A 72 062108
[29]Li G X, Tan H T and Wu S P 2005 Phys. Rev. A 70 064301
[30]Zhou B, Tao R B and Shen S Q 2004 Phys. Rev. A 70 022311
[31]Lloyd S 1998 Phys. Rev. A 57 R1473
[32]Nelson R J, Cory D G and Lloyd S 2000 Phys. Rev. A 61022106
[33]Knill E, Laflamme R, Martinez R and Tseng C H 2000 Nature (London) 404368
[34]Chuang IL, Gershenfeld N, Kubinec M G and Leung D W 1998 Proc. R. Soc. London, Ser. A 454 447
[35]Kuang L M, Chen Z B and Pan J W 2007 Phys. Rev. A 76 052324
[36]Fu L and Liu J 2004 Phys. Rev. A 74 063614
[37]Kapale K T and Dowling J P 2005 Phys. Rev. Lett.95 173601
[38]Yin W, Liang J Q, Yan Q W and Zhang G. F 2004 Phys. Rev. A 70 034304
[39]Kuang L M and Zhou L 2003 Phys. Rev. A 68 043606
[40]Bennett C H, Brassard G, Crepeau C et al 1993 Phys. Rev. Lett.70 1895
[41]Braunstein S L and Kimble H J 1998 Phys. Rev. Lett.80 869
[42]van Loock P and Braunstein S L 2000 Phys. Rev. Lett.84 3482
[43]Furusawa A, S(?)rensen J L, Braunstein S L et al 1998 Science 28 2706
[44]Ralph T C 2000 Phys. Rev. A 61 010303
[45]Pereira S F, Ou Z Y and Kimble H J 2000 Phys. Rev. A 62 042311
[46]Braunstein S L and Kimble H J 2000 Phys. Rev. A 61 042302
[47]Li X Y, Pan Q, Jing J T et al 2002 Phys. Rev. Lett.88 047904
[48]Jing J T, Zhang J, Yan Y et al 2003 Phys. Rev. Lett.90 167903
[49]van Loock P and Braunstein S L 2001 Phys. Rev. Lett.87 247901
[50]Koike S, Takahashi H, Yonezawa H et al 2006 Phys. Rev. Lett.96 060504
[51]Zhang J, Xie C D and Peng K C 2008 Phys. Rev. A 77 022316
[52]Yurke B and Stoler D 1992 Phys. Rev. A 46 2229
[53]Yurke B and Stoler D 1992 Phys. Rev. Lett.68 1251
[54]Zukowski M, Zeilinger A, Home M A and Ekert A 1993 Phys. Rev. Lett.71 4287
[55]Bose S, Vedral V and Knight P L 1998 Phys. Rev. A 57 822
[56]Mattle K, Weinfurter H, Kwiat P G and Zeilinger A 1996 Phys. Rev. Lett.76 4656
[57]Bouwmeester D et al 1997 Nature (London) 390 575
[58]Boschi D, Branca S, De Martini F, Hardy L and Popescu S 1998 Phys. Rev. Lett.80 1121
[59]Jennewein T, Simon C, Weihs G et al 2000 Phys. Rev. Lett.84 4729
[60]Tittel W, Brendel J, Zbinden H and Gisin N 2000 Phys. Rev. Lett.84 4737
[61]Cleve R and Buhrman H 1997 e-print arXiv:quant-ph 9704026
[62]Buhrman H, Cleve R and van Dam W 2001 SIAM J. Comput.30 1829
[63]Brukner C and Vedral V 2004 e-print arXiv:quant-ph 0406040
[64]Brukner C, Paunkovic N, Rudolph T and Vedral V 2005 e-print arXiv:quant-ph 0509123
[65]Venzl H and Freyberger M 2007 Phys. Rev. A 75 042322
[66]Huelga S F, Macchiavello C, Pellizzari T et al 1997 Phys. Rev. Lett.79 3865
[67]Giovannetti V, Lloyd S and Maccone L 2004 Science 306 1330
[68]Jozsa R, Abrams D S, Dowling J P and Williams C P 2000 Phys. Rev. Lett.85 2010
[69]Xiong H, Scully M O and Zubairy M S 2005 Phys. Rev. Lett.94 023601
[70]Hu X M and Zou J H 2008 Phys. Rev. A 78 045801
[71]Li X X and Hu X M 2009 Phys. Rev. A 80 023815
[72]Su X L, Tan A H, Jia X J et al 2007 Phys. Rev. Lett.98 070502
[73]Aoki T, Takei N, Yonezawa H et al 2003 Phys. Rev. Lett.91 080404
[74]Boyd R W 1992 Nonlinear Optics (San Dieag:Academic)
[75]Guzman R, Retamal J C, Solano E, and Zagury N 2006 Phys.Rev. Lett 96 010502
[76]Mancini S 2006 Phys. Rev. A 73 010304(R)
[77]Li G X, Tan H T and Ke S S 2006 Phys. Rev. A 74 012304
[78]Mancini S and Wiseman H M Phys. Rev. A 75 012330
[79]Walls D F and Milburn G J 1994 Quantum Optics (Berlin:Springer-Verlag)
[80]Walls D F 1983 Nature 306 141
[81]Loudon R and Knight P L 1987 J. Mod. Opt.34 709
[82]Caves C M, Thorne K S et al 1980 Rev. Mod. Phys.52 341
[83]Hald J, Soensen J L, Schori C and Polzik E S 1999 Phys. Rev. Lett.83 1319
[84]Lambrecht A, Coudreau T, Steinberg A M and Giacobino E 1996 Europhys. Lett.36 93
[85]Josse V, Dantan A, Vernac L et al 2003 Phys. Rev. Lett.91 103601
[86]Josse V, Dantan A, Bramati A et al 2004 Phys. Rev. Lett.92 123601
[87]Pielawa S, Morigi G, Vitali D and Davidovich L 2007 Phys. Rev. Lett.98 240401
[88]Braunstein S L and van Loock P 2005 Rev. Mod. Phys.77 513
[89]Furusawa A and Takei N 2007 Phys. Rep.443 97
[90]Li X, Pan Q, Jing J et al 2002 Phys. Rev. Lett.88 047904
[91]Silberhorn C, Lam P K, Weiss O, Konig F et al 2001 Phys. Rev. Lett.86 4267
[92]Josse V, Dantan A, Bramati A et al 2004 Phys. Rev. Lett.92 123601
[93]Schumaker B L, Perlmutter S H, Shelby R M and Levenson M D 1987 Phys. Rev. Lett.58 357
[94]Reid M D, Walls D F and Dalton B J Phys. Rev. Lett.55 19851288
[95]Reid M D 1989 Phys. Rev. A 40 913
[96]Scully M O and Zubairy M S 1997 Quantum Optics (Cambridge:Cambridge Uni-versity Press)
[97]Cohen-Tannoudji C, Dupont-Roc J and Grynberg G 1992 Atom-Photon Interactions (New York:Wiley)
[98]Mollow B R 1972 Phys. Rev. A 5 2217
[99]Wu F Y, Ezekiel S, Ducloy M and Mollow B R 1977 Phys. Rev. Lett.38 1077
[100]Agarwal G S 1990 Phys. Rev. A 42 686
[101]Quang T and Freedhoff H 1993 Phys. Rev. A 47 2285
[102]Zhu Y, Wu Q, Morin S E and Mossberg T W 1990 Phys. Rev. Lett 65 1200
[103]Lewenstein M, Zhu Y and Mossberg T W 1990 Phys. Rev. Lett.64 3131
[104]Gauthier D J, Wu Q, Morin S E and Mossberg T W 1992 Phys. Rev. Lett.68 464
[105]Zakrzewski J, Lewenstein M and Mossberg T W 1991 Phys. Rev. A 44 7717 Za-krzewski J, Lewenstein M and Mossberg T W 1991 Phys. Rev. A 44 7732 Zakrzewski J, Lewenstein M and Mossberg T W 1991 Phys. Rev. A 44 7746
[106]James D F V 2000 Fortschr. Phys.48 823
[107]Andersen O K, Lenstra D and Stolte S 1999 Phys. Rev. A 60 1672
[108]Du S, Wen J, Rubin M H and Yin G Y 2007 Phys. Rev. Lett.98 053601
[109]Holland M J, Walls D F and Zoller P 1991 Phys. Rev. Lett.67 1716
[110]Drummond P D and Gardiner C W 1980 J. Phys. A:Math. Gen.13 2353
[111]Drummond P D and Walls D F 1981 Phys. Rev. A 23 2563
[112]Duan L M, Giedke G, Cirac J I and Zoller P 2000 Phys. Rev. Lett.84 2722
[113]Gardiner C W and Zoller P 2000 Quantum Noise 2nd ed (Berlin:Springer)
[114]Carmichael H J 2002 Statistical methods in Quantum Optics 2 ed (Berlin:Springer-Verlag)
[115]Fleischhauer M, Lukin M D, Nikonov D E and Scully M O 1994 Opt. Commun.110 351
[116]Greenberger D M, Home M A, Shimony A and Zeilinger A 1990 Am. J. Phys.58 1131
[117]Zoller P, Beth T, Binosi D, Blatt R, Briegel H, et al 2005 Eur. Phys. J. D 36 203
[118]Briegel H J and Raussendorf R 2001 Phys. Rev. Lett.86 910
[119]Zhang J and Braunstein S L 2006 Phys. Rev. A 73 032318
[120]Hein M, Eisert J and Briegel H J 2004 Phys. Rev. A 69 062311
[121]Hein M, Diir W, Eisert J et al e-print arXiv:quant-ph 0602096
[122]Lloyd S and Braunstein S L 1999 Phys. Rev. Lett.821784
[123]Menicucci N C, van Loock P, Gu M et al 2006 Phys. Rev. Lett.97 110501
[124]Yukawa M, Ukai R, van Loock P and Furusawa A 2008 Phys. Rev. A 78 012301
[125]Lukin M D 2003 Rev. Mod. Phys.75 457
[126]Fleischhauer M, Imamoglu A and Marangos J P 2005 Rev. Mod. Phys.77 633
[127]Hammerer K, Sorensen A S, and Polzik E S 2010 Rev. Mod. Phys.82 1041
[128]Slusher R E, Hollberg L W, Yurke B et al 1986 Phys. Rev. Lett.56 788
[129]Reid M D and Walls D F 1986 Phys. Rev. A 34 4929
[130]Ikram M, Li G X and Zubairy M S 2007 Phys. Rev. A 76 042317
[131]Wu Y and Deng L 2004 Opt. Lett.29 1144
[132]Wu Y and Deng L 2004 Opt. Lett.29 2064
[133]Hu X M,Sun H and Wang F 045807 Phys. Rev. A 82 045807
[134]Tan H T and Li G X 2010 Phys. Rev. A 82 032322
[135]Lu X Y and Wu J 2010 Phys. Rev. A 82 012323
[136]Hau L V, Harris S E, Dutton Z and Behroozi C H 1999 Nature (London) 397 594
[137]Mishina O S, Sheremet A S, Larionov N V and Kupriyanov D V 2010 Opt Spectrosc. 108 313
[138]van Loock P and Furusawa A 2003 Phys. Rev. A 67 052315
[139]Hennrich M, Legero T, Kuhn A and Rempe G 2000 Phys. Rev. Lett.85 4872
[140]S0rensen A S and Molmer K 2002 Phys. Rev. A 66 022314
[141]Liang X, Hu X M and He C 2012 Phys. Rev. A 85 032329
[142]Yu Y B, Sheng J T, and Xiao M 2011 Phys. Rev. A 83 012321
[143]Sargent M III, Scully M O and Lamb W E Jr 1974 Laser Physics (Reading, MA: Addison-Wesley)
[144]Vaidman L 1994 Phys. Rev. A 49 1473
[145]Li P B 2008 Phys. Rev. A 77 015809
[146]Scully M O and Zubairy M S 1987 Phys. Rev. A 35 752
[147]Bergou J, Orszag M and Scully M O 1988 Phys. Rev. A 38 768
[148]Lu N 1992 Phys. Rev. A 45 8154
[149]Meystre P and Sargent M Ⅲ 1999 Element of Quantum Optics 3rd edn (Berlin: Springer)
[150]Cheng G L, Hu X M, Zhong W X and Li Q 2008 Phys. Rev. A 78 033811
[151]Qamar S, Ghafoor F, Hillery M and Zubairy M S 2008 Phys. Rev. A 77 062308
[152]Parkins A S, Marte P, Zoller P and Kimble H J 1993 Phys. Rev. Lett.71 3095
[153]Law C K and Eberly J H 1996 Phys. Rev. Lett.76,1055
[154]Wellens Th, Buchleitner A, Kummerer K et al 2000 Phys. Rev. Lett.85 3361
[155]Matsukevich D N, Chaneliere T, Bhattacharya M et al 2005 Phys. Rev. Lett.95 040405
[156]Raab E, Prentiss M, Cable A et al 1987 Phys. Rev. Lett.59 2631
[157]Monroe C, Swann W, Robinson H and Wieman C 1990 Phys. Rev. Lett.65 1571
[158]Liu C, Dutton Z, Behroozi C H and Hau L V 2001 Nature (London) 409 490
[159]Kang H and Zhu Y 2003 Phys. Rev. Lett.91 093601
[160]Chen Y F, Wang C Y, Wang S H and Yu I A 2006 Phys. Rev. Lett.96 043603
[161]Kitching J and Hollberg L 1999 Phys. Rev. A 59 4685
[162]von Cube Ch, et al 2006 Fortschr. Phys.54 726
[163]Klinner J, Lindholdt M, Nagorny B et al 2006 Phys. Rev. Lett.96 023002
[2]Einstein A, Podolsky B and Rosen N 1935 Phys. Rev.47 777
[3]Schrodinger E 1935 Naturwiss 23 807
[4]Bell J S 1964 Physics 1 195
[5]Gisin N 1991 Phys. Lett. A 154 201
[6]Popescu S and Rohrlich D 1992 Phys. Lett. A 166 293
[7]Kocher C A and Commins E D 1967 Phys. Rev. Lett.18 575
[8]Freedman S J and Clauser J F 1972 Phys. Rev. Lett.28 938
[9]Aspect A, Dalibard J and Roger G 1982 Phys. Rev. Lett.49 1804
[10]Aspect A, Grangier P and Roger G 1981 Phys. Rev. Lett.47 460
[11]Ou Z Y and Mandel L 1988 Phys. Rev. Lett.61 50
[12]Kwiat P G, Mattle K, Weinfurter H et al 1995 Phys. Rev. Lett.75 4337
[13]Tittel W, Brendel J, Zbinden H and Gisin N 1998 Phys. Rev. Lett.81 3563
[14]Tittel W, Brendel J, Gisin N and Zbinden H 1999 Phys. Rev. A 59 4150
[15]Weihs G, Jennewein T, Simon C et al 1998 Phys. Rev. Lett.81 5039
[16]Rowe M A et al 2001 Nature (London) 409 791
[17]Hasegawa Y, Loidl R, Badurek G et al 2004 J. Opt. B:Quantum Semiclassical Opt. 6S7
[18]Bovino F A, Giardina M, Svozil K and Vedral V 2006 e-print arXiv:quant-ph 0603167
[19]Ursin R et al 2007 Nat. Phys.3 481
[20]Gonta D, Pritzsche S and Radtke T 2003 Phys. Rev. A 77 062312
[21]Morrison S and Parkins A S 2006 Phys. Rev. A 74043810
[22]Shu J, Zou X B, Xiao Y F and Guo G C 2006 Phys. Rev. A 74 044301
[23]Zhang X L, Guo K L and Feng M 2006 Phys. Rev. A 74 024303
[24]Zhou D L, Sun B, Sun C P and You L 2005 Phys. Rev. A 72 040302
[25]Zou X B and Mathis W 2004 Phys. Rev. A 70 035802
[26]Li G X and Wu S P 2005 Phys. Rev. A 72 064304
[27]Haljan P C, Lee P J, Brickman K A et al 2005 Phys. Rev. A 72 062316
[28]Yang W X, Zhan Z M and Li J H 2005 Phys. Rev. A 72 062108
[29]Li G X, Tan H T and Wu S P 2005 Phys. Rev. A 70 064301
[30]Zhou B, Tao R B and Shen S Q 2004 Phys. Rev. A 70 022311
[31]Lloyd S 1998 Phys. Rev. A 57 R1473
[32]Nelson R J, Cory D G and Lloyd S 2000 Phys. Rev. A 61022106
[33]Knill E, Laflamme R, Martinez R and Tseng C H 2000 Nature (London) 404368
[34]Chuang IL, Gershenfeld N, Kubinec M G and Leung D W 1998 Proc. R. Soc. London, Ser. A 454 447
[35]Kuang L M, Chen Z B and Pan J W 2007 Phys. Rev. A 76 052324
[36]Fu L and Liu J 2004 Phys. Rev. A 74 063614
[37]Kapale K T and Dowling J P 2005 Phys. Rev. Lett.95 173601
[38]Yin W, Liang J Q, Yan Q W and Zhang G. F 2004 Phys. Rev. A 70 034304
[39]Kuang L M and Zhou L 2003 Phys. Rev. A 68 043606
[40]Bennett C H, Brassard G, Crepeau C et al 1993 Phys. Rev. Lett.70 1895
[41]Braunstein S L and Kimble H J 1998 Phys. Rev. Lett.80 869
[42]van Loock P and Braunstein S L 2000 Phys. Rev. Lett.84 3482
[43]Furusawa A, S(?)rensen J L, Braunstein S L et al 1998 Science 28 2706
[44]Ralph T C 2000 Phys. Rev. A 61 010303
[45]Pereira S F, Ou Z Y and Kimble H J 2000 Phys. Rev. A 62 042311
[46]Braunstein S L and Kimble H J 2000 Phys. Rev. A 61 042302
[47]Li X Y, Pan Q, Jing J T et al 2002 Phys. Rev. Lett.88 047904
[48]Jing J T, Zhang J, Yan Y et al 2003 Phys. Rev. Lett.90 167903
[49]van Loock P and Braunstein S L 2001 Phys. Rev. Lett.87 247901
[50]Koike S, Takahashi H, Yonezawa H et al 2006 Phys. Rev. Lett.96 060504
[51]Zhang J, Xie C D and Peng K C 2008 Phys. Rev. A 77 022316
[52]Yurke B and Stoler D 1992 Phys. Rev. A 46 2229
[53]Yurke B and Stoler D 1992 Phys. Rev. Lett.68 1251
[54]Zukowski M, Zeilinger A, Home M A and Ekert A 1993 Phys. Rev. Lett.71 4287
[55]Bose S, Vedral V and Knight P L 1998 Phys. Rev. A 57 822
[56]Mattle K, Weinfurter H, Kwiat P G and Zeilinger A 1996 Phys. Rev. Lett.76 4656
[57]Bouwmeester D et al 1997 Nature (London) 390 575
[58]Boschi D, Branca S, De Martini F, Hardy L and Popescu S 1998 Phys. Rev. Lett.80 1121
[59]Jennewein T, Simon C, Weihs G et al 2000 Phys. Rev. Lett.84 4729
[60]Tittel W, Brendel J, Zbinden H and Gisin N 2000 Phys. Rev. Lett.84 4737
[61]Cleve R and Buhrman H 1997 e-print arXiv:quant-ph 9704026
[62]Buhrman H, Cleve R and van Dam W 2001 SIAM J. Comput.30 1829
[63]Brukner C and Vedral V 2004 e-print arXiv:quant-ph 0406040
[64]Brukner C, Paunkovic N, Rudolph T and Vedral V 2005 e-print arXiv:quant-ph 0509123
[65]Venzl H and Freyberger M 2007 Phys. Rev. A 75 042322
[66]Huelga S F, Macchiavello C, Pellizzari T et al 1997 Phys. Rev. Lett.79 3865
[67]Giovannetti V, Lloyd S and Maccone L 2004 Science 306 1330
[68]Jozsa R, Abrams D S, Dowling J P and Williams C P 2000 Phys. Rev. Lett.85 2010
[69]Xiong H, Scully M O and Zubairy M S 2005 Phys. Rev. Lett.94 023601
[70]Hu X M and Zou J H 2008 Phys. Rev. A 78 045801
[71]Li X X and Hu X M 2009 Phys. Rev. A 80 023815
[72]Su X L, Tan A H, Jia X J et al 2007 Phys. Rev. Lett.98 070502
[73]Aoki T, Takei N, Yonezawa H et al 2003 Phys. Rev. Lett.91 080404
[74]Boyd R W 1992 Nonlinear Optics (San Dieag:Academic)
[75]Guzman R, Retamal J C, Solano E, and Zagury N 2006 Phys.Rev. Lett 96 010502
[76]Mancini S 2006 Phys. Rev. A 73 010304(R)
[77]Li G X, Tan H T and Ke S S 2006 Phys. Rev. A 74 012304
[78]Mancini S and Wiseman H M Phys. Rev. A 75 012330
[79]Walls D F and Milburn G J 1994 Quantum Optics (Berlin:Springer-Verlag)
[80]Walls D F 1983 Nature 306 141
[81]Loudon R and Knight P L 1987 J. Mod. Opt.34 709
[82]Caves C M, Thorne K S et al 1980 Rev. Mod. Phys.52 341
[83]Hald J, Soensen J L, Schori C and Polzik E S 1999 Phys. Rev. Lett.83 1319
[84]Lambrecht A, Coudreau T, Steinberg A M and Giacobino E 1996 Europhys. Lett.36 93
[85]Josse V, Dantan A, Vernac L et al 2003 Phys. Rev. Lett.91 103601
[86]Josse V, Dantan A, Bramati A et al 2004 Phys. Rev. Lett.92 123601
[87]Pielawa S, Morigi G, Vitali D and Davidovich L 2007 Phys. Rev. Lett.98 240401
[88]Braunstein S L and van Loock P 2005 Rev. Mod. Phys.77 513
[89]Furusawa A and Takei N 2007 Phys. Rep.443 97
[90]Li X, Pan Q, Jing J et al 2002 Phys. Rev. Lett.88 047904
[91]Silberhorn C, Lam P K, Weiss O, Konig F et al 2001 Phys. Rev. Lett.86 4267
[92]Josse V, Dantan A, Bramati A et al 2004 Phys. Rev. Lett.92 123601
[93]Schumaker B L, Perlmutter S H, Shelby R M and Levenson M D 1987 Phys. Rev. Lett.58 357
[94]Reid M D, Walls D F and Dalton B J Phys. Rev. Lett.55 19851288
[95]Reid M D 1989 Phys. Rev. A 40 913
[96]Scully M O and Zubairy M S 1997 Quantum Optics (Cambridge:Cambridge Uni-versity Press)
[97]Cohen-Tannoudji C, Dupont-Roc J and Grynberg G 1992 Atom-Photon Interactions (New York:Wiley)
[98]Mollow B R 1972 Phys. Rev. A 5 2217
[99]Wu F Y, Ezekiel S, Ducloy M and Mollow B R 1977 Phys. Rev. Lett.38 1077
[100]Agarwal G S 1990 Phys. Rev. A 42 686
[101]Quang T and Freedhoff H 1993 Phys. Rev. A 47 2285
[102]Zhu Y, Wu Q, Morin S E and Mossberg T W 1990 Phys. Rev. Lett 65 1200
[103]Lewenstein M, Zhu Y and Mossberg T W 1990 Phys. Rev. Lett.64 3131
[104]Gauthier D J, Wu Q, Morin S E and Mossberg T W 1992 Phys. Rev. Lett.68 464
[105]Zakrzewski J, Lewenstein M and Mossberg T W 1991 Phys. Rev. A 44 7717 Za-krzewski J, Lewenstein M and Mossberg T W 1991 Phys. Rev. A 44 7732 Zakrzewski J, Lewenstein M and Mossberg T W 1991 Phys. Rev. A 44 7746
[106]James D F V 2000 Fortschr. Phys.48 823
[107]Andersen O K, Lenstra D and Stolte S 1999 Phys. Rev. A 60 1672
[108]Du S, Wen J, Rubin M H and Yin G Y 2007 Phys. Rev. Lett.98 053601
[109]Holland M J, Walls D F and Zoller P 1991 Phys. Rev. Lett.67 1716
[110]Drummond P D and Gardiner C W 1980 J. Phys. A:Math. Gen.13 2353
[111]Drummond P D and Walls D F 1981 Phys. Rev. A 23 2563
[112]Duan L M, Giedke G, Cirac J I and Zoller P 2000 Phys. Rev. Lett.84 2722
[113]Gardiner C W and Zoller P 2000 Quantum Noise 2nd ed (Berlin:Springer)
[114]Carmichael H J 2002 Statistical methods in Quantum Optics 2 ed (Berlin:Springer-Verlag)
[115]Fleischhauer M, Lukin M D, Nikonov D E and Scully M O 1994 Opt. Commun.110 351
[116]Greenberger D M, Home M A, Shimony A and Zeilinger A 1990 Am. J. Phys.58 1131
[117]Zoller P, Beth T, Binosi D, Blatt R, Briegel H, et al 2005 Eur. Phys. J. D 36 203
[118]Briegel H J and Raussendorf R 2001 Phys. Rev. Lett.86 910
[119]Zhang J and Braunstein S L 2006 Phys. Rev. A 73 032318
[120]Hein M, Eisert J and Briegel H J 2004 Phys. Rev. A 69 062311
[121]Hein M, Diir W, Eisert J et al e-print arXiv:quant-ph 0602096
[122]Lloyd S and Braunstein S L 1999 Phys. Rev. Lett.821784
[123]Menicucci N C, van Loock P, Gu M et al 2006 Phys. Rev. Lett.97 110501
[124]Yukawa M, Ukai R, van Loock P and Furusawa A 2008 Phys. Rev. A 78 012301
[125]Lukin M D 2003 Rev. Mod. Phys.75 457
[126]Fleischhauer M, Imamoglu A and Marangos J P 2005 Rev. Mod. Phys.77 633
[127]Hammerer K, Sorensen A S, and Polzik E S 2010 Rev. Mod. Phys.82 1041
[128]Slusher R E, Hollberg L W, Yurke B et al 1986 Phys. Rev. Lett.56 788
[129]Reid M D and Walls D F 1986 Phys. Rev. A 34 4929
[130]Ikram M, Li G X and Zubairy M S 2007 Phys. Rev. A 76 042317
[131]Wu Y and Deng L 2004 Opt. Lett.29 1144
[132]Wu Y and Deng L 2004 Opt. Lett.29 2064
[133]Hu X M,Sun H and Wang F 045807 Phys. Rev. A 82 045807
[134]Tan H T and Li G X 2010 Phys. Rev. A 82 032322
[135]Lu X Y and Wu J 2010 Phys. Rev. A 82 012323
[136]Hau L V, Harris S E, Dutton Z and Behroozi C H 1999 Nature (London) 397 594
[137]Mishina O S, Sheremet A S, Larionov N V and Kupriyanov D V 2010 Opt Spectrosc. 108 313
[138]van Loock P and Furusawa A 2003 Phys. Rev. A 67 052315
[139]Hennrich M, Legero T, Kuhn A and Rempe G 2000 Phys. Rev. Lett.85 4872
[140]S0rensen A S and Molmer K 2002 Phys. Rev. A 66 022314
[141]Liang X, Hu X M and He C 2012 Phys. Rev. A 85 032329
[142]Yu Y B, Sheng J T, and Xiao M 2011 Phys. Rev. A 83 012321
[143]Sargent M III, Scully M O and Lamb W E Jr 1974 Laser Physics (Reading, MA: Addison-Wesley)
[144]Vaidman L 1994 Phys. Rev. A 49 1473
[145]Li P B 2008 Phys. Rev. A 77 015809
[146]Scully M O and Zubairy M S 1987 Phys. Rev. A 35 752
[147]Bergou J, Orszag M and Scully M O 1988 Phys. Rev. A 38 768
[148]Lu N 1992 Phys. Rev. A 45 8154
[149]Meystre P and Sargent M Ⅲ 1999 Element of Quantum Optics 3rd edn (Berlin: Springer)
[150]Cheng G L, Hu X M, Zhong W X and Li Q 2008 Phys. Rev. A 78 033811
[151]Qamar S, Ghafoor F, Hillery M and Zubairy M S 2008 Phys. Rev. A 77 062308
[152]Parkins A S, Marte P, Zoller P and Kimble H J 1993 Phys. Rev. Lett.71 3095
[153]Law C K and Eberly J H 1996 Phys. Rev. Lett.76,1055
[154]Wellens Th, Buchleitner A, Kummerer K et al 2000 Phys. Rev. Lett.85 3361
[155]Matsukevich D N, Chaneliere T, Bhattacharya M et al 2005 Phys. Rev. Lett.95 040405
[156]Raab E, Prentiss M, Cable A et al 1987 Phys. Rev. Lett.59 2631
[157]Monroe C, Swann W, Robinson H and Wieman C 1990 Phys. Rev. Lett.65 1571
[158]Liu C, Dutton Z, Behroozi C H and Hau L V 2001 Nature (London) 409 490
[159]Kang H and Zhu Y 2003 Phys. Rev. Lett.91 093601
[160]Chen Y F, Wang C Y, Wang S H and Yu I A 2006 Phys. Rev. Lett.96 043603
[161]Kitching J and Hollberg L 1999 Phys. Rev. A 59 4685
[162]von Cube Ch, et al 2006 Fortschr. Phys.54 726
[163]Klinner J, Lindholdt M, Nagorny B et al 2006 Phys. Rev. Lett.96 023002