变频率辐射场对量子系统非经典特性的调控
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摘要
在量子光学中,运用Jaynes-Cummings模型对光场与原子相互作用系统的非经典特性进行研究一直受到人们的广泛关注。研究光场与原子相互作用的Jaynes-Cummings模型中原子和光场状态的运动规律及其非经典效应是量子光学的重要内容之一。本论文应用全量子理论和数值计算方法来研究频率变化的光场与原子相互作用系统的特性,得出了一系列有意义的结论。
第1章简要介绍光场与原子相互作用的基本理论：量子光学的发展历史、辐射场的量子化、量子光学中的几种非经典态、光场与原子作用的理论模型(J-C模型)等；
第2章,我们运用全量子理论,在分析了辐射场与二能级原子相互作用过程中系统的哈密顿量的基础上,找出影响辐射场与原子间的耦合系数的因素；再通过光学谐振腔腔镜振动机制研究腔镜振动与辐射场频率之间的关系以及场频变化函数和谐振腔体积变化函数之间的关系；最后总结得出耦合系数与辐射场频率变化函数间的关系；。
第3章是在第2章的基础上,在旋波近似下,利用推广的J-C模型,考虑光场的频率随时间按照正弦函数的形式作小量变化,采用数值计算的方法,研究分析二项式光场与二能级原子相互作用体系中光场的振幅平方压缩效应。最终的研究结果表明：场频率的变化对光场的振幅平方压缩的深度和周期性都存在影响；
第4章对全文进行了总结并对相关问题进行了展望。
In the context of quantum optics, the study of quantum features for the interaction between optical fields and atoms has attracted much attention. It is one of the most important contents of quantum optics to study the dynamics and the non-classical features of optical fields and atoms in the Jaynes-Cummings interaction model. In this thesis, the dynamical features of time-varying-frequency radiation field interacting with a two-level atom have been studied by using the quantum theory and the numerical simulation method. A series of significant results are obtained.
In chapter 1, the elementary theories of the interaction between optical fields and atoms were introduced, such as the history of quantum optics, quantization of radiation fields, several kinds of non-classical states and an important interaction model (Janynes-Cummings model).
In chapter 2, we studied the interaction Hamiltonian of the two-level atom and a single-mode radiation field, and tried to find the factors that determine the coupling coefficient between cavity modes and atoms. By introducing the vibration mechanism of one cavity mirror, we first got the connection between the frequency of the cavity mode and the vibration of the cavity mirror, and then we found the relationship between the time-varying function of the mode frequency and that of the volume of the cavity. Finally, we got the exact relationship between the time-varying function of the mode frequency and the coupling coefficient between cavity modes field and atoms.
In chapter 3, the effect of the amplitude-squared squeezing of the time-varying-frequency field interacting with a two-level atom is studied by using the numerical method. Here, the field is in binomial state, and the interaction can be described by a generalized J-C model under rotating wave approximation. The results showed that the depth and the period of the amplitude-squared squeezing effect of optical field are determined by the time-dependent frequency variance of the optical field.
In chapter 4, we summarized the main results and made an outlook for our further investigations in the near future.
第1章简要介绍光场与原子相互作用的基本理论：量子光学的发展历史、辐射场的量子化、量子光学中的几种非经典态、光场与原子作用的理论模型(J-C模型)等；
第2章,我们运用全量子理论,在分析了辐射场与二能级原子相互作用过程中系统的哈密顿量的基础上,找出影响辐射场与原子间的耦合系数的因素；再通过光学谐振腔腔镜振动机制研究腔镜振动与辐射场频率之间的关系以及场频变化函数和谐振腔体积变化函数之间的关系；最后总结得出耦合系数与辐射场频率变化函数间的关系；。
第3章是在第2章的基础上,在旋波近似下,利用推广的J-C模型,考虑光场的频率随时间按照正弦函数的形式作小量变化,采用数值计算的方法,研究分析二项式光场与二能级原子相互作用体系中光场的振幅平方压缩效应。最终的研究结果表明：场频率的变化对光场的振幅平方压缩的深度和周期性都存在影响；
第4章对全文进行了总结并对相关问题进行了展望。
In the context of quantum optics, the study of quantum features for the interaction between optical fields and atoms has attracted much attention. It is one of the most important contents of quantum optics to study the dynamics and the non-classical features of optical fields and atoms in the Jaynes-Cummings interaction model. In this thesis, the dynamical features of time-varying-frequency radiation field interacting with a two-level atom have been studied by using the quantum theory and the numerical simulation method. A series of significant results are obtained.
In chapter 1, the elementary theories of the interaction between optical fields and atoms were introduced, such as the history of quantum optics, quantization of radiation fields, several kinds of non-classical states and an important interaction model (Janynes-Cummings model).
In chapter 2, we studied the interaction Hamiltonian of the two-level atom and a single-mode radiation field, and tried to find the factors that determine the coupling coefficient between cavity modes and atoms. By introducing the vibration mechanism of one cavity mirror, we first got the connection between the frequency of the cavity mode and the vibration of the cavity mirror, and then we found the relationship between the time-varying function of the mode frequency and that of the volume of the cavity. Finally, we got the exact relationship between the time-varying function of the mode frequency and the coupling coefficient between cavity modes field and atoms.
In chapter 3, the effect of the amplitude-squared squeezing of the time-varying-frequency field interacting with a two-level atom is studied by using the numerical method. Here, the field is in binomial state, and the interaction can be described by a generalized J-C model under rotating wave approximation. The results showed that the depth and the period of the amplitude-squared squeezing effect of optical field are determined by the time-dependent frequency variance of the optical field.
In chapter 4, we summarized the main results and made an outlook for our further investigations in the near future.
引文
[1]. Stoler D. Equivalence Classes of Minimum-Uncertainty Packets [J]. Phys. Rev. D,1970,1,3217-3219;
[2]. Stoler D. Equivalence Classes of Minimum-Uncertainty Packets.Ⅱ[J]. Phys. Rev. D,1971,4,1925-1926
[3]. Walls, D. F. and Zoller, P. Reduced Quantum Fluctuations in Resonance Fluorescence [J]. Phys. Rev.Lett.,1981,47(10),709-711
[4]. Agarwal G S, Puri R R. Cooperative behavior of atoms irradiated by broadband squeezed light[J]. Phys.Rev.A,1990,41,3782
[5]. Wineland D. J, Bollinger J. J. Itano W. M. Squeeze atomic state and projection noise in spectroscopy [J]. Phys. Rev. A,1994,50,67-88
[6]. Li X S, Lin D L, George T. F. Squeezing of atomic variables in the one-photon and two-photon Jaynes-Cummings model [J]. Phys. Rev. A,1989,40,2504;
[7]. Ashraf M. M., Razmi M. S. K. Atomic-diople squeezing and emission spectra of the nondegenerate two-photon Jaynes-Cummings model [J]. Phys. Rev. A, 1992.45,8121;
[8]. Zhou P, Peng J. S. Dipole squeezing in the two-photon Jaynes- Cummings model with superposition state preparation [J]. Phys. Rev. A,1991,44,3331;
[9]. Wodkiewicz K, Knight P L, Buckle S J, Barnett S. M. Squeezing and superposition states [J]. Phys. Rev. A,1987,35,2567
[10]. Kuzmieh A, Molmer K, Polzik E S. Spin squeezing in an ensemble of atoms illuminated with squeezed light [J].Phys. Rev. Lett.,1997,79,4782
[11]. Saito H, Ueda M. Quantum-Controlled Few-Photon State Generated by Squeezed Atoms [J]. Phys. Rev. Lett.,1997,79,3869;
[12]. Saito H, Ueda M. Squeezed few-photo states of the field generated from squeezed atoms [J]. Phys. Rev. A,1999,59,3959
[13]. Jaynes E T, Cummings, Comparison of quantum and semiclassicalradiation theories with application to beam maser [J]. Proc.IEEE.,1963,51 (1):89-109
[14]. Eberly J. H, Narozhny N B, Sanchez-Nondragon J J. Periodic spontaneous collapse and revival in a simple quantum model[J]. Phys. Rev. Lett.,1980,44 (20):1323-1326
[15]. 周鹏,彭金生.双光子Jaynes-Cummings模型中原子的压缩效应[J].物理学报,1989,38(12)：2044-2048
[16]. Shumovsky A S, Fam Le Kien, Aliskenderov E I. Squeezing in the multiphoton Jaynes-Cummings model[J].Phys.Lett.A,1987,124 (6):351-354
[17]. 李高翔,彭金生.论Janyes-Cummings模型中原子偶极压缩和光场压缩间的关联[J].物理学报,1995,44(10)：1670-1678
[18]. Zhou P, Hu Z L, Peng J S. Effect of Atomic Coherence on the Collapses and Revivals in Some Generalized Janyes-Cummings Models [J]. J.Mod. Opt, 1992,39(1):49-62
[19]. Zhu S.Y. Non-Classical Features in the three-level Janyes-Cummings ModeI[J]. J.Mod.Opt,1989,36(4):499-513
[20]. Schlicher R R.Jaynes-Cummings model with atomic motion[J].Opt Commun. 1989,70:97
[21]. Joshi A,Lawande S V.Squeezing and quasiprobabilities for a two-photon Jaynes- Cummings model with atomic motion.Int J Mod Phys B,1992,6:3539
[22]. Bartzis V.Generalized Jaynes-Cummings model with atomic motion[J]. Physica A,1992,180:428
[23]. 刘小娟,王琴惠.具有原子运动的双光子J-C模型的场熵和薛定谔猫态[J].量子光学学报,1999,5(1)：1-9
[24]. 廖湘萍,方卯发.原子质心运动和场模结构对场熵压缩特性的影响[J].量子电子学报,2005,22(2)：212-216
[25]. 刘堂昆,王继锁,詹明生.含原子运动的模型中的量子态保真度[J].原子与分子物理学报,2001,18(1)58-63
[26].姜春蕾,方卯发,吴珍珍.双纠缠原子在耗散腔场中的纠缠动力学[J].物理学报,2006,55(9)：4647-4651
[27]. 王忠纯.外场驱动对Tavis-Cummings模型中量子态保真度的影响[J].物理学报,2006,55(9)：4624-4630
[28]. Yang Y P, Xie J P, Li G X, Hong C. Interactions of a two-level atom and a field with a time-varying frequency [J]. Phys. Rev. A.2004,69:053406
[29]. 卢道明.场频率随时间变化对原子偶极压缩效应的影响[J].原子与分子物理学报.2007,24(4)：827-832
[30]. 卢道明,频率变化场与原子相互作用系统中原子的信息熵压缩[J].原子与分子物理学报.2009,26(6)：1098-1106
[31]. 许静平,羊业平.场频率变化时原子与场的相互作用,物理学报.2004,53(7)：2139-2144
[32]. 贾飞,谢双媛,羊亚平.非旋波近似下频率变化的场与原子的相互作用[J].物理学报.2006,55(11)：5835-5841
[33]. 蔡勋明,范梦慧.频率变化的相十态光场中两原子纠缠演化[J].光学学报.2009,29(9)：2570-2576
[34]. 江洵,场频率变化时多光子J-C模型中原子的动力学特性[J].光谱实验室2006,23(5)：1001-1005
[35]. 贾金平,变耦合系数的简并拉曼耦合J-C模型中场熵的演化[J].量子光学学报2006,12(4)：212-217
[36]. Yuen H P. Two-photon coherent states of the radiation field [J]. Phys. Rev. A. 1976,13(6):2226
[37]. 李福利.高等激光物理学[M].高等教育出版社2006.7第2版.
[38]. 于祖荣,量子光学中的非经典态[J]物理学进展19(1),1999,3,72-95
[39]. Knight P L, Milonni P W.The Rabi frequency in optical spectra[J]. Phys. Rep., 1980,66:21
[40]. Yoo Y L, Eberly.Dynamical theory of an atom with two or three levels interacting with quantum cavity field[J].Phys.Rep.,1985,118(5):239
[41]. Shore B W, Knight P L.The Jaynes-Cummings model[J].Mod.Opt.,1993,40(7): 1195
[42]. 汪贤才,曹卓良.双模光场与运动原子作用系统的反聚束效应[J].原子分子 学报,2007,24(4)：785-792
[43]. Caves C M. Quantum-mechanical noise in an interferometer [J]. Phys. Rev. D. 1981,23(8):1693-1708
[44]. Gea-Banacloche J, Leuchs G. Squeezed states for interferometric gravitational-wave detectors [J]. J. Mod. Opt..1987,34(6,7):793-811
[45]. Jaynes E. T, Cummings F. W. Comparison of quantum and semiclassical radiation theory with application to the beam maser[J]. Proc. IEEE. 1963,51:89
[46]. 赵加强,夏云杰.Kerr介质中k光了J-C模型原子信息熵的演化特性[J].原子与分子物理学报.2004.21(4).700-704
[47]. 王海军,高云峰,闫丽华.大失谐J-C模型中腔耗散对量子态保真度的影响[J].原子与分子物理学报,2009,26(5)：882-886
[48]. 刘万芳,李春杰,章礼华等.几类相十态的量子保真度[J],原子与分子物理学报,2009,26(4)：327-332
[49]. 张成强,谭霞,夏云杰.存在相位退相干时原子与光场相互作用的纠缠演化和保持[J].原子与分子物理学报,2007,24(4)：757-761
[50]. 秦东青,单传家,夏云杰.粒子数光场中原子纠缠的演化特性[J].原子与分子物理学报,2007,24(5)：1021-1027
[51]. 邹艳Kerr介质中V型三能级原子与双模奇偶纠缠相十光场相互作用的纠缠特性[J].原子与分子物理学报,2008,25(5)：1079-1085
[52]. 蔡新华、彭光含、乔闹生,利用两能级原了与腔场的相互作用转移纠缠[J].原子与分子物理学报,2009,26(6)：1093-1097
[53]. 韩峰,夏云杰,杜少将,基于Tavis-Cummings模型实现非定域三原子系统量了特性的远程控制[J].原了与分了物理学报.2009,26(6)：1107-1113
[54].张桂明,李悦科,高云峰Kerr效应对非线性J-C模型辐射谱的影响[J].原子与分子物理学报,2007,24(6)：1316-1320
[55]. 何林生,双光了过程中光场振幅平方压缩[J].物理学报,1991,40(6)：904-911
[56]. 宋同强,葛广英.双光子Tavis-Cummings模型中辐射场的振幅平方压缩 效应[J].量子电子学.1993,10(3)：286-288
[57]. Mark Hillery. Squeezing of the square of the field amplitude in second harmonic generation. Opt. Comm. [J].1987,62(2):135-138
[58]. Mark Hillery. Amplitude-squared squeezing of the electromagnetic field [J]. Phys. Rev. A.1987,36(8):3796-3803
[59]. 郑小虎,曹卓良.双模纠缠相干光场与V型三能级原了相互作用系统的光场压缩效应[J].量子电子学报.2004,21(6)：778-782
[60]. Walls D W. Squeezed state of light [J]. Nature.1983,306:141-146
[61]. 黄春佳,周明等.单模辐射场与耦合双原了相互作用系统中场熵的压缩特性[J].物理学报.2002,51(4)：805-808
[62]. 汪贤才,曹卓良.二项式光场与运动三型三能级原子相互作用系统的光场压缩效应[J].吉林大学学报(理学版).2006,44(3)：445-449
[63]. 邓文基,刘平,徐晓.混合态的不确定关系与压缩效应[J].物理学报.2004,53(11)：3368-3672
[64].周清平.原子相干性对光场振幅平方压缩的影响[J].量子光学学报.1998,4(4)：223-228
[65].方卯发,陈菊梅.熵测不准关系与光场的熵压缩[J].光学学报.2001,21(1)：8-12
[66].刘王云,杨志勇,安毓英等.与两等同Bell态纠缠原子相互作用光场的量子场熵[J].光子学报.37(3)2008：594-599
[67].廖湘萍,方卯发,与量了光场相互作用的运动原子的熵压缩[J],光学学报,2004,24(7)：983-988
[68].王忠纯,刘成林.原子纠缠对驱动T-C模型中量子态保真度的影响[J].量子电子学报.2008,25(2)：191-197
[69]. 谢利军,张登玉,唐世清.辐射场中二能级原子的量子态保真度[J].量子电子学报.2008,25(6)：719-725
[70]. 夏云杰, 王光辉,杜少将.双模最小关联混合态作为量子信道实现量子隐形传态的保真度[J].物理学报.2007,56(8)：4431-4436
[71]. 张成强,谭霞,夏云杰 双模相干场与Bell态原子多光子作用的原子布居 数演化[J]量子电子学报2006,23(6)：825-829
[72]. M.Sargent Ⅲ, M. O. Scully and W. E. Lamb, Laser physics [M], Addison-Wesley, Mass.,1974.
[73]. Yang Yaping, Xu Jingping, Li Gaoxiang, et al. Interactions of a two-level atom and a field with a time-varying frequency [J].Phys. Rev. A.2004,69, 053406.
[74]. 郭光灿,量子光学的回顾和展望[J],物理,1992,21(1)：32-37
[75]. 杨志勇,侯洵,21世纪量子光学领域的若干重大核心问题展望-兼论量子光学的发展动态与发展方向[J],商洛师范专科学校学报,2000,14(专辑)：1-52
[76]. Jaynes E T. Cummings F W. Comparison of quantum and semiclassical to the beam maser[M]. Proc. IEEE,1963,51(1):89-110
[77]. 李前树,邵彬,邹健,场与介观约瑟夫森结的相互作用[M],北京,科学出版社,2002,12
[78]. 彭金生,共振荧光与超荧光[M],北京,科学出版社,1993,11
[2]. Stoler D. Equivalence Classes of Minimum-Uncertainty Packets.Ⅱ[J]. Phys. Rev. D,1971,4,1925-1926
[3]. Walls, D. F. and Zoller, P. Reduced Quantum Fluctuations in Resonance Fluorescence [J]. Phys. Rev.Lett.,1981,47(10),709-711
[4]. Agarwal G S, Puri R R. Cooperative behavior of atoms irradiated by broadband squeezed light[J]. Phys.Rev.A,1990,41,3782
[5]. Wineland D. J, Bollinger J. J. Itano W. M. Squeeze atomic state and projection noise in spectroscopy [J]. Phys. Rev. A,1994,50,67-88
[6]. Li X S, Lin D L, George T. F. Squeezing of atomic variables in the one-photon and two-photon Jaynes-Cummings model [J]. Phys. Rev. A,1989,40,2504;
[7]. Ashraf M. M., Razmi M. S. K. Atomic-diople squeezing and emission spectra of the nondegenerate two-photon Jaynes-Cummings model [J]. Phys. Rev. A, 1992.45,8121;
[8]. Zhou P, Peng J. S. Dipole squeezing in the two-photon Jaynes- Cummings model with superposition state preparation [J]. Phys. Rev. A,1991,44,3331;
[9]. Wodkiewicz K, Knight P L, Buckle S J, Barnett S. M. Squeezing and superposition states [J]. Phys. Rev. A,1987,35,2567
[10]. Kuzmieh A, Molmer K, Polzik E S. Spin squeezing in an ensemble of atoms illuminated with squeezed light [J].Phys. Rev. Lett.,1997,79,4782
[11]. Saito H, Ueda M. Quantum-Controlled Few-Photon State Generated by Squeezed Atoms [J]. Phys. Rev. Lett.,1997,79,3869;
[12]. Saito H, Ueda M. Squeezed few-photo states of the field generated from squeezed atoms [J]. Phys. Rev. A,1999,59,3959
[13]. Jaynes E T, Cummings, Comparison of quantum and semiclassicalradiation theories with application to beam maser [J]. Proc.IEEE.,1963,51 (1):89-109
[14]. Eberly J. H, Narozhny N B, Sanchez-Nondragon J J. Periodic spontaneous collapse and revival in a simple quantum model[J]. Phys. Rev. Lett.,1980,44 (20):1323-1326
[15]. 周鹏,彭金生.双光子Jaynes-Cummings模型中原子的压缩效应[J].物理学报,1989,38(12)：2044-2048
[16]. Shumovsky A S, Fam Le Kien, Aliskenderov E I. Squeezing in the multiphoton Jaynes-Cummings model[J].Phys.Lett.A,1987,124 (6):351-354
[17]. 李高翔,彭金生.论Janyes-Cummings模型中原子偶极压缩和光场压缩间的关联[J].物理学报,1995,44(10)：1670-1678
[18]. Zhou P, Hu Z L, Peng J S. Effect of Atomic Coherence on the Collapses and Revivals in Some Generalized Janyes-Cummings Models [J]. J.Mod. Opt, 1992,39(1):49-62
[19]. Zhu S.Y. Non-Classical Features in the three-level Janyes-Cummings ModeI[J]. J.Mod.Opt,1989,36(4):499-513
[20]. Schlicher R R.Jaynes-Cummings model with atomic motion[J].Opt Commun. 1989,70:97
[21]. Joshi A,Lawande S V.Squeezing and quasiprobabilities for a two-photon Jaynes- Cummings model with atomic motion.Int J Mod Phys B,1992,6:3539
[22]. Bartzis V.Generalized Jaynes-Cummings model with atomic motion[J]. Physica A,1992,180:428
[23]. 刘小娟,王琴惠.具有原子运动的双光子J-C模型的场熵和薛定谔猫态[J].量子光学学报,1999,5(1)：1-9
[24]. 廖湘萍,方卯发.原子质心运动和场模结构对场熵压缩特性的影响[J].量子电子学报,2005,22(2)：212-216
[25]. 刘堂昆,王继锁,詹明生.含原子运动的模型中的量子态保真度[J].原子与分子物理学报,2001,18(1)58-63
[26].姜春蕾,方卯发,吴珍珍.双纠缠原子在耗散腔场中的纠缠动力学[J].物理学报,2006,55(9)：4647-4651
[27]. 王忠纯.外场驱动对Tavis-Cummings模型中量子态保真度的影响[J].物理学报,2006,55(9)：4624-4630
[28]. Yang Y P, Xie J P, Li G X, Hong C. Interactions of a two-level atom and a field with a time-varying frequency [J]. Phys. Rev. A.2004,69:053406
[29]. 卢道明.场频率随时间变化对原子偶极压缩效应的影响[J].原子与分子物理学报.2007,24(4)：827-832
[30]. 卢道明,频率变化场与原子相互作用系统中原子的信息熵压缩[J].原子与分子物理学报.2009,26(6)：1098-1106
[31]. 许静平,羊业平.场频率变化时原子与场的相互作用,物理学报.2004,53(7)：2139-2144
[32]. 贾飞,谢双媛,羊亚平.非旋波近似下频率变化的场与原子的相互作用[J].物理学报.2006,55(11)：5835-5841
[33]. 蔡勋明,范梦慧.频率变化的相十态光场中两原子纠缠演化[J].光学学报.2009,29(9)：2570-2576
[34]. 江洵,场频率变化时多光子J-C模型中原子的动力学特性[J].光谱实验室2006,23(5)：1001-1005
[35]. 贾金平,变耦合系数的简并拉曼耦合J-C模型中场熵的演化[J].量子光学学报2006,12(4)：212-217
[36]. Yuen H P. Two-photon coherent states of the radiation field [J]. Phys. Rev. A. 1976,13(6):2226
[37]. 李福利.高等激光物理学[M].高等教育出版社2006.7第2版.
[38]. 于祖荣,量子光学中的非经典态[J]物理学进展19(1),1999,3,72-95
[39]. Knight P L, Milonni P W.The Rabi frequency in optical spectra[J]. Phys. Rep., 1980,66:21
[40]. Yoo Y L, Eberly.Dynamical theory of an atom with two or three levels interacting with quantum cavity field[J].Phys.Rep.,1985,118(5):239
[41]. Shore B W, Knight P L.The Jaynes-Cummings model[J].Mod.Opt.,1993,40(7): 1195
[42]. 汪贤才,曹卓良.双模光场与运动原子作用系统的反聚束效应[J].原子分子 学报,2007,24(4)：785-792
[43]. Caves C M. Quantum-mechanical noise in an interferometer [J]. Phys. Rev. D. 1981,23(8):1693-1708
[44]. Gea-Banacloche J, Leuchs G. Squeezed states for interferometric gravitational-wave detectors [J]. J. Mod. Opt..1987,34(6,7):793-811
[45]. Jaynes E. T, Cummings F. W. Comparison of quantum and semiclassical radiation theory with application to the beam maser[J]. Proc. IEEE. 1963,51:89
[46]. 赵加强,夏云杰.Kerr介质中k光了J-C模型原子信息熵的演化特性[J].原子与分子物理学报.2004.21(4).700-704
[47]. 王海军,高云峰,闫丽华.大失谐J-C模型中腔耗散对量子态保真度的影响[J].原子与分子物理学报,2009,26(5)：882-886
[48]. 刘万芳,李春杰,章礼华等.几类相十态的量子保真度[J],原子与分子物理学报,2009,26(4)：327-332
[49]. 张成强,谭霞,夏云杰.存在相位退相干时原子与光场相互作用的纠缠演化和保持[J].原子与分子物理学报,2007,24(4)：757-761
[50]. 秦东青,单传家,夏云杰.粒子数光场中原子纠缠的演化特性[J].原子与分子物理学报,2007,24(5)：1021-1027
[51]. 邹艳Kerr介质中V型三能级原子与双模奇偶纠缠相十光场相互作用的纠缠特性[J].原子与分子物理学报,2008,25(5)：1079-1085
[52]. 蔡新华、彭光含、乔闹生,利用两能级原了与腔场的相互作用转移纠缠[J].原子与分子物理学报,2009,26(6)：1093-1097
[53]. 韩峰,夏云杰,杜少将,基于Tavis-Cummings模型实现非定域三原子系统量了特性的远程控制[J].原了与分了物理学报.2009,26(6)：1107-1113
[54].张桂明,李悦科,高云峰Kerr效应对非线性J-C模型辐射谱的影响[J].原子与分子物理学报,2007,24(6)：1316-1320
[55]. 何林生,双光了过程中光场振幅平方压缩[J].物理学报,1991,40(6)：904-911
[56]. 宋同强,葛广英.双光子Tavis-Cummings模型中辐射场的振幅平方压缩 效应[J].量子电子学.1993,10(3)：286-288
[57]. Mark Hillery. Squeezing of the square of the field amplitude in second harmonic generation. Opt. Comm. [J].1987,62(2):135-138
[58]. Mark Hillery. Amplitude-squared squeezing of the electromagnetic field [J]. Phys. Rev. A.1987,36(8):3796-3803
[59]. 郑小虎,曹卓良.双模纠缠相干光场与V型三能级原了相互作用系统的光场压缩效应[J].量子电子学报.2004,21(6)：778-782
[60]. Walls D W. Squeezed state of light [J]. Nature.1983,306:141-146
[61]. 黄春佳,周明等.单模辐射场与耦合双原了相互作用系统中场熵的压缩特性[J].物理学报.2002,51(4)：805-808
[62]. 汪贤才,曹卓良.二项式光场与运动三型三能级原子相互作用系统的光场压缩效应[J].吉林大学学报(理学版).2006,44(3)：445-449
[63]. 邓文基,刘平,徐晓.混合态的不确定关系与压缩效应[J].物理学报.2004,53(11)：3368-3672
[64].周清平.原子相干性对光场振幅平方压缩的影响[J].量子光学学报.1998,4(4)：223-228
[65].方卯发,陈菊梅.熵测不准关系与光场的熵压缩[J].光学学报.2001,21(1)：8-12
[66].刘王云,杨志勇,安毓英等.与两等同Bell态纠缠原子相互作用光场的量子场熵[J].光子学报.37(3)2008：594-599
[67].廖湘萍,方卯发,与量了光场相互作用的运动原子的熵压缩[J],光学学报,2004,24(7)：983-988
[68].王忠纯,刘成林.原子纠缠对驱动T-C模型中量子态保真度的影响[J].量子电子学报.2008,25(2)：191-197
[69]. 谢利军,张登玉,唐世清.辐射场中二能级原子的量子态保真度[J].量子电子学报.2008,25(6)：719-725
[70]. 夏云杰, 王光辉,杜少将.双模最小关联混合态作为量子信道实现量子隐形传态的保真度[J].物理学报.2007,56(8)：4431-4436
[71]. 张成强,谭霞,夏云杰 双模相干场与Bell态原子多光子作用的原子布居 数演化[J]量子电子学报2006,23(6)：825-829
[72]. M.Sargent Ⅲ, M. O. Scully and W. E. Lamb, Laser physics [M], Addison-Wesley, Mass.,1974.
[73]. Yang Yaping, Xu Jingping, Li Gaoxiang, et al. Interactions of a two-level atom and a field with a time-varying frequency [J].Phys. Rev. A.2004,69, 053406.
[74]. 郭光灿,量子光学的回顾和展望[J],物理,1992,21(1)：32-37
[75]. 杨志勇,侯洵,21世纪量子光学领域的若干重大核心问题展望-兼论量子光学的发展动态与发展方向[J],商洛师范专科学校学报,2000,14(专辑)：1-52
[76]. Jaynes E T. Cummings F W. Comparison of quantum and semiclassical to the beam maser[M]. Proc. IEEE,1963,51(1):89-110
[77]. 李前树,邵彬,邹健,场与介观约瑟夫森结的相互作用[M],北京,科学出版社,2002,12
[78]. 彭金生,共振荧光与超荧光[M],北京,科学出版社,1993,11