光场与三能级原子相互作用的熵动力学
|
摘要
1989年,Phoenix和Knight等人将熵理论应用于量子光学领域,研究光场与原子相互作用时的信息关联与演化,显示出很大的优越性。由于熵函数自动包含了量子系统密度矩阵的全部统计矩,它不仅是一种十分灵敏的量子态纯度的操作测量,还被用于描述量子系统的纠缠程度,同时也是解释量子系统动力学特性的重要工具,在量子信息领域有着广泛的应用。另一方面,原子—光场纠缠特性的研究对原子、光场量子态的制备以及原子和光场的量子信息和量子计算领域有着广泛的应用。近十五年来,人们对于标准JCM以及各种推广形式的JCM中熵动力学作了大量的研究。但是,目前这些研究工作的一个共同特点是:(1)原子与场的耦合系数简单地看作常数处理;(2)仅限于考虑原子运动与模结构的二能级原子的讨论。本文将从这两方面作有意义的扩展工作。
本文首先运用全量子理论,(1)导出了考虑原子运动的∧-型三能级原子与单模场在共振情况下相互作用系统中的波函数;借助远离共振的条件Δ>>|ω_1-ω_2|(即Δ>>0),也推导出了考虑原子运动与模结构的简并拉曼耦合J-C模型中的波函数;(2)导出了在共振情况且原子-场耦合系数随时间线形变化时∨-型三能级原子与单模场相互作用系统中的波函数,也推导出了变耦合系数的简并拉曼耦合J-C模型中的波函数。然后,利用P-K熵理论,借助已导出的波函数,具体讨论了不同的初始光场、原子运动与模结构以及耦合系数的变化对原子—场相互作用中场(原子)熵的影响。
研究表明:(1)原子运动导致场熵演化具有周期性,这种周期性并不依赖场的统计分布和强度而是依赖于原子运动和模结构参数εp;(2)不论是共振情况还是远离共振情况,在选取合适的参数εp(这种选取在实验上是可能的)时,都能得到较长时间的纯态光场;(3)通过∧-型三能级原子与单模场相互作用的演化过程并不能直接产生薛定谔猫态;(4)初始光场统计性质的不同对场熵产生较大的影响;(5)线形调制使场熵呈现的完美周期性振荡遭到破坏,当原子-场耦合系数变化缓慢时,原子进入统计混合态的速度被减缓;而当原子-场耦
In 1989,the entropy theory has been applied to quantum optics by Phoenix and Knight, they have shown the entropy theory is a convenient and sensitive measure of the information concerning and evolution about interaction of the field with the atom. Entropy not only is a very useful operational measureof the purity of the quantum state,which automatically includes all moments of the density operator,but is applied to describe the degree of entanglement in quantum system,so has a intensive use in quantum information.On the other hand,the study on the properties of the entanglement between the field and the atom will have a entensive use in performing quantum state about the field and the atom and the field and atom of quantum information and computing.Much study has been done on entropic dynamics in the JCM and all kinds of generalized JCM,since 15 years recently.But,at present a trait of these study work in commom is: (i) the atom-field coupling coefficients is simply regarded to a constant;(ii) only limited to the effects of atomic motion and field mode structure on the two-level atom.In this paper,a significative generalized work will be done from the two aspects.In this paper,at first,we bring to bear the full quantum theory,(i) to educe the wave function of the system considering the interaction of a ∧-type three-level moving atom with field under on-resonance condition And the wave function in degenerate raman process JCM considering atomic motion and field mode structure by using the far-off- resonance condition;(ii) to educe the wave function of the system considering the interaction of a V -type three-level atom with field with a time-dependent atom-field coupling under on-resonance condition and the wave function in degenerate raman process JCM with a time-dependent atom-field coupling. Second,we utilize entropy theory,in virtue of the wave function,the effects of the different initial field, the atomic motion and field-mode structure and the time-dependent atom-field coupling
coefficient on the field entropy is discussed at length.The results show that: (1) the atomic motion leads to the periodic evolution of the field entropy,this periodicity does not depend on the statistical distribution and the intensity of the initial field mode,but depends on the atomic velocity v,the length of the cavity L and the field-mode structure parameters p .(2) both on-resonance condition and far-off-resonance condition,when making a suitable choice for parameter sp (this choice is experimentally possible),we can get pure field state for a long time.(3) there are no Schrodinger-cat states in the evolution processes of interaction of the field with the A-type three-level atom.(4) the difference of initial field will produce great effect in field entropy.(5) the perfect periodicity of field entropy has been destroyed due the linear modulation, When the atom-field coupling coefficient changes slowly,the speed of atom entering the statistical state;When the atom-field coupling coefficient changes rapidly,the oscillating frequency of the evolution of entropy is fastened.
本文首先运用全量子理论,(1)导出了考虑原子运动的∧-型三能级原子与单模场在共振情况下相互作用系统中的波函数;借助远离共振的条件Δ>>|ω_1-ω_2|(即Δ>>0),也推导出了考虑原子运动与模结构的简并拉曼耦合J-C模型中的波函数;(2)导出了在共振情况且原子-场耦合系数随时间线形变化时∨-型三能级原子与单模场相互作用系统中的波函数,也推导出了变耦合系数的简并拉曼耦合J-C模型中的波函数。然后,利用P-K熵理论,借助已导出的波函数,具体讨论了不同的初始光场、原子运动与模结构以及耦合系数的变化对原子—场相互作用中场(原子)熵的影响。
研究表明:(1)原子运动导致场熵演化具有周期性,这种周期性并不依赖场的统计分布和强度而是依赖于原子运动和模结构参数εp;(2)不论是共振情况还是远离共振情况,在选取合适的参数εp(这种选取在实验上是可能的)时,都能得到较长时间的纯态光场;(3)通过∧-型三能级原子与单模场相互作用的演化过程并不能直接产生薛定谔猫态;(4)初始光场统计性质的不同对场熵产生较大的影响;(5)线形调制使场熵呈现的完美周期性振荡遭到破坏,当原子-场耦合系数变化缓慢时,原子进入统计混合态的速度被减缓;而当原子-场耦
In 1989,the entropy theory has been applied to quantum optics by Phoenix and Knight, they have shown the entropy theory is a convenient and sensitive measure of the information concerning and evolution about interaction of the field with the atom. Entropy not only is a very useful operational measureof the purity of the quantum state,which automatically includes all moments of the density operator,but is applied to describe the degree of entanglement in quantum system,so has a intensive use in quantum information.On the other hand,the study on the properties of the entanglement between the field and the atom will have a entensive use in performing quantum state about the field and the atom and the field and atom of quantum information and computing.Much study has been done on entropic dynamics in the JCM and all kinds of generalized JCM,since 15 years recently.But,at present a trait of these study work in commom is: (i) the atom-field coupling coefficients is simply regarded to a constant;(ii) only limited to the effects of atomic motion and field mode structure on the two-level atom.In this paper,a significative generalized work will be done from the two aspects.In this paper,at first,we bring to bear the full quantum theory,(i) to educe the wave function of the system considering the interaction of a ∧-type three-level moving atom with field under on-resonance condition And the wave function in degenerate raman process JCM considering atomic motion and field mode structure by using the far-off- resonance condition;(ii) to educe the wave function of the system considering the interaction of a V -type three-level atom with field with a time-dependent atom-field coupling under on-resonance condition and the wave function in degenerate raman process JCM with a time-dependent atom-field coupling. Second,we utilize entropy theory,in virtue of the wave function,the effects of the different initial field, the atomic motion and field-mode structure and the time-dependent atom-field coupling
coefficient on the field entropy is discussed at length.The results show that: (1) the atomic motion leads to the periodic evolution of the field entropy,this periodicity does not depend on the statistical distribution and the intensity of the initial field mode,but depends on the atomic velocity v,the length of the cavity L and the field-mode structure parameters p .(2) both on-resonance condition and far-off-resonance condition,when making a suitable choice for parameter sp (this choice is experimentally possible),we can get pure field state for a long time.(3) there are no Schrodinger-cat states in the evolution processes of interaction of the field with the A-type three-level atom.(4) the difference of initial field will produce great effect in field entropy.(5) the perfect periodicity of field entropy has been destroyed due the linear modulation, When the atom-field coupling coefficient changes slowly,the speed of atom entering the statistical state;When the atom-field coupling coefficient changes rapidly,the oscillating frequency of the evolution of entropy is fastened.
引文
[1] Jaynes E T, Cummings F W.Comparision of and semiclassical radiation theories with application to beam maser [J].Proc.IEEE, 1963,51 (1):89～109
[2] 王义道.激光冷却与捕陷原子的方法——1997年诺贝尔物理学奖介绍[J].物理,1998,27(3):131～136
[3] 戴闻.超流He中波色—爱因斯坦凝聚的直接证据[J].物理,1998,27(9):574～575
[4] Agarwal G S.Vacuum-field rabi oscillations of atoms in a cavity.[J].Opt.Soc. Am.B,1 985,2:480～485
[5] Buzek V.Light squeeing in the Jaynes-Cummings with intensity-dependent couping[J].mod.Opt,1989,36(9):1151～1162
[6] Brune M,Schmidt-kaler F.Quantum rabioscillation:a direct test of field quantization in acavity [J].Phys.Rev.Lett,1996,76(11):1800～1803
[7] 姚德民,郭光灿.非经典态光场的判据[J].物理学报,1988,37(3):463～468
[8] Rempe G, Walther H, Klein N.Observation of quantum collapse and revival in a one-atom maser [J].Phys.Rev.Lett, 1987,58(4):353～356
[9] 李福利.腔损对单原子微激射器产生稳定四阶与振幅平方压缩态的影响[J].物理学报,1996,45(4):563～572
[10] 任珉,马爱群,郑太立.单原子微激射器中原子的压缩效应的研究[J].量子电子学,1995,12(1):6～10
[11] Fu-li Li,Xiao-shen Li,Lin D L.Squeezing of many-atom radiation in an optical cavity [J].Phys.Rev.(A),1990,41 (5):2712～2717
[12] 李福利,黄庆.利用单原子微激射器产生非经典腔场 [J].量子光学学报,1995,1(1):21～26
[13] 杨志勇,侯洵.光子学与光子技术对中西部科技经济发展的影响 [J].西北大学学报(自然科学版),1998,28(6):475～479
[14] 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[J].商洛师范专科学校学报,2000,14(9):1～52
[15] Gama H.Matrix treatment of partial coherence [J]. Progress in Optics, 1964, (3):189～301
[16] Aravind P K, Hirschfelder J O.J.Phys.Chem., 1984,88:4788～4792
[17] Phoenix S J D, Knight P L.Flucution and entropy in models quantum optical resonance [J].Ann.Phys(NY), 1988,186:381～407
[18] Phoenix S J D, Knight P L.Establishment of an entangled atom-field state in the Jaynes-Cummings model [J].Phys.Rev.(A), 1991 ,A1 (6):6023～6029
[19] 石名俊,杜江峰,朱栋培.量子纯态的纠缠度 [J].物理学报,2000,49(5):825～829
[20] Phoenix S J D, Knight P L.Periodicity, phase,and entropy in models of two-photon reasonance [J].Opt.Soc.Am.(B), 1990,B7(1): 116～124
[21] Clausius R,ibid., 125,400(1865)
[22] 王彬.熵与信息.西安:西北工业大学出版社,1994.18
[23] Shannon C E.A Mathematical Theory of Communication [J].Bell.Syste. Tech, 1948,27:623～656
[24] 胡国定.信息论中Shannon定理的三种反定理 [J].数学学报,1961,11(3):260～294
[25] 王维.熵理论的哲学意义[J].自然辨证法通迅,1987,(3):132～136
[26] Holton G.物理科学的概念和理论导轮(上),人民教育出版社,1983:438
[27] Von Neumann J.Mathematical foundations of quantum mechanics (Princeton university press,Princeton,NJ, 1955)
[28] Barnett S M, Phoenix S J D.Entropy as a measure of quantum optical correlation [J].Phys.Rev.(A), 1989,40(5):2404～2409
[29] Mao-Fa Fang,Guang-Hui Zhou.Influence of atomic coherence on the evolution of field of field entropy in multiphoton processes [J].Physics letters A,1994,184:397～402
[30] 方卯发,周鹏.多光子Jaynes-Cummings 模型场熵的演化 [J].光学学报,1993,13(9):800～804
[31] 刘翔.双模双光子Jaynes-Cummings模型中场与原子的缠绕 [J].量子电子学,1995,12(3):326～330
[32] 苏春清,柳永亮.双模SU(1,1)相干态与原子相互作用过程的场熵演化[J].量子光学学报,1998,4(3):149～153
[33] 刘翔,方卯发,刘安玲.非耦合双模场中级联三能级原子的熵特性[J].量子电子学报,2002,19(1):43～47
[34] Mao-Fa Fang,Hui-en Liu.Properties of entropy and phase of the field in the two-photon Jaynes-Cummings model [J].Physics letters A, 1995,200:250～258
[35] 方卯发,刘慧恩.附加克尔介质Jaynes-Cummings模型场熵的演化[J].光学学报,1994,14(5):475～479
[36] 方卯发,周鹏.附加克尔介质双光子Jaynes-Cummings模型场熵演化[J].物理学报,1994,43(4):570～579
[37] 刘金明,陶向阳,刘三秋等。克尔介质中场与级联三能级原子相互作用的熵特性 [J].光学学报,2000,20(11):1456～1460
[38] 方卯发.非旋波近似下Jaynes-Cummings模型中的场熵演化 [J].物理学报,1994,43(11):1776～1785
[39] 刘素梅.非旋波近似下光场与级联型三能级原子相互作用系统的场熵演化特性[J].量子电子学报,2003,20(6):725～732
[40] Mao-Fa Fang,Xiang Liu.Influence of the Stark shift on the evolution field entropy and entanglement in two-photon processes [J].Physics letters A,1996,210:11～20
[41] 刘翔,方卯发.简并拉曼过程中斯塔克位移对原子反转及场熵的影响[J].光学学报,1996,16(4):435～440
[42] 敖胜美,周石伦,曾高坚.非简并拉曼过程中交流斯塔克位移对场熵和缠绕的影响[J].物理学报,2001,50(1):52～58
[43] Mao-Fa Fang.Effects of atomic motion and field mode structure on the field entropy and Schrodinger-cat states in the Jaynes-Cummings model [J].Physica A,1998,259:193～204
[44] 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
[45] 刘翔,方卯发.光场与级联型三能级原子相互作用时的熵特性和薛定谔猫态[J].物理学报,2000,49(9):1707～1713
[46] 方卯发.依赖强度耦合J-C模型场熵的演化[J].光学学报,1995,15(3):296～300
[47] 黄燕霞,郝东山,汪毅.Kerr效应对非线形Jaynes-Cummings模型场熵和缠结的影响[J].光子学报,2002,31(12):1448～1452
[48] 周清平.依赖强度耦合多光子过程中的缠绕与薛定谔猫态[J].光学学报,1998,18(6):712～716
[49] 黄春佳,贺惠勇,孔凡志等.光场与V型三能级原子依赖强度耦合系统场熵的演化特性 [J].物理学报,2004,53(8):2539～2544
[50] 黄生训,方卯发.双光子Tavis-Cummings模型场熵的演化[J].量子电子学,1996,13(3):245～251
[51] 黄春佳,贺惠勇,孔凡志等.Tavis-Cummings模型中原子间偶极相互作用对场熵演化特性的影响[J].物理学报,2002,51(5):1049～1053
[52] 衣学喜,孙昌璞.原子间的偶极相互作用对原子的动力学特性及场熵演化特性的影响[J].科学通报,1996,41(13):1165～1169
[53] 黄燕霞,郭光灿.压缩真空态Jaynes-Cummings模型中场熵演化的特性[J].量子光学学报,1996,2(2):97～104
[54] 黄生训,方卯发.多光子过程中单模热辐射场与原子相互作用的场熵特性[J].量子电子学,1995,12(2):212～216
[55] 赖振讲,刘自信.附加Kerr介质非关联双模相干态场与V型三能级原子的相互作用系统中原子(场)的熵特性 [J].物理学报,2000,49(9):1714～1718
[56] Diedrich F, Bergquist J C,Itano W M,Wineland D J.Laser cooling to the zero-point energy of motion [J].Phys Rev Lett,1989,62(4):403～406
[57] Schlicher R R.Jaynes-Cummings model with atomic motion [J]. Opt Commun, 1989,70(2):97～102
[58] Joshi A,Lawande S V. Effect of atomic motion on Ryderg atoms unde-r going two-transitions in a lossless cavity [J].Phys Rev(A), 1990,42 (3): 1752～1758
[59] Lawande A J S V.Squeezing and quasiprobabilities for a two-photon Jaynes-Cummings model with atomic motion [J].Mod Phys(B),1992,6(10): 3539～3545
[60] Bartzis V. Generalized Jaynes-Cummings model with atom motion [J]. Physica(A),1992, 180(3):428～434
[61] 刘堂昆,王继锁,詹明生.含原子运动的Jaynes-Cummings模型中的量子态保真度[J].原子分子物理学报,2001,18(1):58～63
[62] 张少武,是度芳.级联三能级运动原子与单模场相互作用系统中光子的反聚束效应[J].量子电子学报,2003,20(4):449～453
[63] Zhu Ai-Dong,Zhang Shou. Influence of atomic motion on the population and dipole squeezing of a cascade three-level atom in cavity field. Chinese Physicas,2004,13(8): 1276～1284
[64] 张智明.非简并Raman耦合模型的改进型有效哈密顿量[J].量子光学学报,1996,2(1):32～36
[65] W.H.Louisell.Quantum statistical properties of radiation (Wiley, New York, 1973)
[66] Joshi A,Puri R R.Characteristics of Rabi oscillations in the two-mode squeezing state of the field.Phys.Rev.(A), 1990,42(7):4336～4348
[67] Puff R R,Agarwal G S.Finite-Q cavity electrodynamics:dynamical and statistical aspects [J].Phys.Rev.(A), 1987,35(8):3433～3442
[68] Brune M,Schmidt-Kaler F, Maali A etal.Quantum Rabi oscillation: a direct test of field quantization in a cavity [J].Phys.Rev.Lett., 1996,76(11): 1800～1804
[69] Joshi A,Puri R R. Dynamical evolution of the two-photo Jaynes-Cummings model in a Kerr-like medium [J].Phys.Rev.(A),1992, 45(7): 5056～5062
[70] Lei Xu,Zhi-Ming Zhang. Modified effective Hamiltonian for degenerate Raman process. Z.Phys.(B), 1994,B95(2):507～510
[71] Amitab H,Joshi A, Lawanda S V.Generalized Jaynes-Cummings model with a time-dependent atom-field couping [J].Phys.Rev.(A), 1993,48(3): 2276～2284
[72] 许静平,羊亚平.压缩态初始光场下变耦合系数的J-C模型[J].光学学报,2004,24(11):1577～1580
[73] 许静平,羊亚平.压缩态光场变耦合系数双光子J-C模型性质[J].光学学报,2005,25(2):251～255
[74] 朱小芹.耦合系数与时间有关的三能级原子同辐射场的相互作用[J].光学学报,1997,17(5):520～525
[75] 郭光灿.量子光学.北京:高等教育出版社,1990.227～227
[76] 罗耕贤,郭光灿.压缩态J-C模型中的崩塌—复原现象[J].光学学报,1990,10(1):1～5
[77] Agarwal G S.Field-correlation effects is multiphoton absorption process [J].Phys.Rev. (A), 1970,A1 (5): 1445～1459
[78] Joshi A, Lanwande S V.Effects of dipole interaction on the collapse-revival phenomenon of Rabi oscillations [J].Mod.Opt., 1991,38(5): 1407～1413
[79] 张立辉,李高翔,彭金生.位相损耗腔中简并双光子拉曼耦合系统中的熵特性[J].物理学报,2002,51(3):541～546
[2] 王义道.激光冷却与捕陷原子的方法——1997年诺贝尔物理学奖介绍[J].物理,1998,27(3):131～136
[3] 戴闻.超流He中波色—爱因斯坦凝聚的直接证据[J].物理,1998,27(9):574～575
[4] Agarwal G S.Vacuum-field rabi oscillations of atoms in a cavity.[J].Opt.Soc. Am.B,1 985,2:480～485
[5] Buzek V.Light squeeing in the Jaynes-Cummings with intensity-dependent couping[J].mod.Opt,1989,36(9):1151～1162
[6] Brune M,Schmidt-kaler F.Quantum rabioscillation:a direct test of field quantization in acavity [J].Phys.Rev.Lett,1996,76(11):1800～1803
[7] 姚德民,郭光灿.非经典态光场的判据[J].物理学报,1988,37(3):463～468
[8] Rempe G, Walther H, Klein N.Observation of quantum collapse and revival in a one-atom maser [J].Phys.Rev.Lett, 1987,58(4):353～356
[9] 李福利.腔损对单原子微激射器产生稳定四阶与振幅平方压缩态的影响[J].物理学报,1996,45(4):563～572
[10] 任珉,马爱群,郑太立.单原子微激射器中原子的压缩效应的研究[J].量子电子学,1995,12(1):6～10
[11] Fu-li Li,Xiao-shen Li,Lin D L.Squeezing of many-atom radiation in an optical cavity [J].Phys.Rev.(A),1990,41 (5):2712～2717
[12] 李福利,黄庆.利用单原子微激射器产生非经典腔场 [J].量子光学学报,1995,1(1):21～26
[13] 杨志勇,侯洵.光子学与光子技术对中西部科技经济发展的影响 [J].西北大学学报(自然科学版),1998,28(6):475～479
[14] 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[J].商洛师范专科学校学报,2000,14(9):1～52
[15] Gama H.Matrix treatment of partial coherence [J]. Progress in Optics, 1964, (3):189～301
[16] Aravind P K, Hirschfelder J O.J.Phys.Chem., 1984,88:4788～4792
[17] Phoenix S J D, Knight P L.Flucution and entropy in models quantum optical resonance [J].Ann.Phys(NY), 1988,186:381～407
[18] Phoenix S J D, Knight P L.Establishment of an entangled atom-field state in the Jaynes-Cummings model [J].Phys.Rev.(A), 1991 ,A1 (6):6023～6029
[19] 石名俊,杜江峰,朱栋培.量子纯态的纠缠度 [J].物理学报,2000,49(5):825～829
[20] Phoenix S J D, Knight P L.Periodicity, phase,and entropy in models of two-photon reasonance [J].Opt.Soc.Am.(B), 1990,B7(1): 116～124
[21] Clausius R,ibid., 125,400(1865)
[22] 王彬.熵与信息.西安:西北工业大学出版社,1994.18
[23] Shannon C E.A Mathematical Theory of Communication [J].Bell.Syste. Tech, 1948,27:623～656
[24] 胡国定.信息论中Shannon定理的三种反定理 [J].数学学报,1961,11(3):260～294
[25] 王维.熵理论的哲学意义[J].自然辨证法通迅,1987,(3):132～136
[26] Holton G.物理科学的概念和理论导轮(上),人民教育出版社,1983:438
[27] Von Neumann J.Mathematical foundations of quantum mechanics (Princeton university press,Princeton,NJ, 1955)
[28] Barnett S M, Phoenix S J D.Entropy as a measure of quantum optical correlation [J].Phys.Rev.(A), 1989,40(5):2404～2409
[29] Mao-Fa Fang,Guang-Hui Zhou.Influence of atomic coherence on the evolution of field of field entropy in multiphoton processes [J].Physics letters A,1994,184:397～402
[30] 方卯发,周鹏.多光子Jaynes-Cummings 模型场熵的演化 [J].光学学报,1993,13(9):800～804
[31] 刘翔.双模双光子Jaynes-Cummings模型中场与原子的缠绕 [J].量子电子学,1995,12(3):326～330
[32] 苏春清,柳永亮.双模SU(1,1)相干态与原子相互作用过程的场熵演化[J].量子光学学报,1998,4(3):149～153
[33] 刘翔,方卯发,刘安玲.非耦合双模场中级联三能级原子的熵特性[J].量子电子学报,2002,19(1):43～47
[34] Mao-Fa Fang,Hui-en Liu.Properties of entropy and phase of the field in the two-photon Jaynes-Cummings model [J].Physics letters A, 1995,200:250～258
[35] 方卯发,刘慧恩.附加克尔介质Jaynes-Cummings模型场熵的演化[J].光学学报,1994,14(5):475～479
[36] 方卯发,周鹏.附加克尔介质双光子Jaynes-Cummings模型场熵演化[J].物理学报,1994,43(4):570～579
[37] 刘金明,陶向阳,刘三秋等。克尔介质中场与级联三能级原子相互作用的熵特性 [J].光学学报,2000,20(11):1456～1460
[38] 方卯发.非旋波近似下Jaynes-Cummings模型中的场熵演化 [J].物理学报,1994,43(11):1776～1785
[39] 刘素梅.非旋波近似下光场与级联型三能级原子相互作用系统的场熵演化特性[J].量子电子学报,2003,20(6):725～732
[40] Mao-Fa Fang,Xiang Liu.Influence of the Stark shift on the evolution field entropy and entanglement in two-photon processes [J].Physics letters A,1996,210:11～20
[41] 刘翔,方卯发.简并拉曼过程中斯塔克位移对原子反转及场熵的影响[J].光学学报,1996,16(4):435～440
[42] 敖胜美,周石伦,曾高坚.非简并拉曼过程中交流斯塔克位移对场熵和缠绕的影响[J].物理学报,2001,50(1):52～58
[43] Mao-Fa Fang.Effects of atomic motion and field mode structure on the field entropy and Schrodinger-cat states in the Jaynes-Cummings model [J].Physica A,1998,259:193～204
[44] 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
[45] 刘翔,方卯发.光场与级联型三能级原子相互作用时的熵特性和薛定谔猫态[J].物理学报,2000,49(9):1707～1713
[46] 方卯发.依赖强度耦合J-C模型场熵的演化[J].光学学报,1995,15(3):296～300
[47] 黄燕霞,郝东山,汪毅.Kerr效应对非线形Jaynes-Cummings模型场熵和缠结的影响[J].光子学报,2002,31(12):1448～1452
[48] 周清平.依赖强度耦合多光子过程中的缠绕与薛定谔猫态[J].光学学报,1998,18(6):712～716
[49] 黄春佳,贺惠勇,孔凡志等.光场与V型三能级原子依赖强度耦合系统场熵的演化特性 [J].物理学报,2004,53(8):2539～2544
[50] 黄生训,方卯发.双光子Tavis-Cummings模型场熵的演化[J].量子电子学,1996,13(3):245～251
[51] 黄春佳,贺惠勇,孔凡志等.Tavis-Cummings模型中原子间偶极相互作用对场熵演化特性的影响[J].物理学报,2002,51(5):1049～1053
[52] 衣学喜,孙昌璞.原子间的偶极相互作用对原子的动力学特性及场熵演化特性的影响[J].科学通报,1996,41(13):1165～1169
[53] 黄燕霞,郭光灿.压缩真空态Jaynes-Cummings模型中场熵演化的特性[J].量子光学学报,1996,2(2):97～104
[54] 黄生训,方卯发.多光子过程中单模热辐射场与原子相互作用的场熵特性[J].量子电子学,1995,12(2):212～216
[55] 赖振讲,刘自信.附加Kerr介质非关联双模相干态场与V型三能级原子的相互作用系统中原子(场)的熵特性 [J].物理学报,2000,49(9):1714～1718
[56] Diedrich F, Bergquist J C,Itano W M,Wineland D J.Laser cooling to the zero-point energy of motion [J].Phys Rev Lett,1989,62(4):403～406
[57] Schlicher R R.Jaynes-Cummings model with atomic motion [J]. Opt Commun, 1989,70(2):97～102
[58] Joshi A,Lawande S V. Effect of atomic motion on Ryderg atoms unde-r going two-transitions in a lossless cavity [J].Phys Rev(A), 1990,42 (3): 1752～1758
[59] Lawande A J S V.Squeezing and quasiprobabilities for a two-photon Jaynes-Cummings model with atomic motion [J].Mod Phys(B),1992,6(10): 3539～3545
[60] Bartzis V. Generalized Jaynes-Cummings model with atom motion [J]. Physica(A),1992, 180(3):428～434
[61] 刘堂昆,王继锁,詹明生.含原子运动的Jaynes-Cummings模型中的量子态保真度[J].原子分子物理学报,2001,18(1):58～63
[62] 张少武,是度芳.级联三能级运动原子与单模场相互作用系统中光子的反聚束效应[J].量子电子学报,2003,20(4):449～453
[63] Zhu Ai-Dong,Zhang Shou. Influence of atomic motion on the population and dipole squeezing of a cascade three-level atom in cavity field. Chinese Physicas,2004,13(8): 1276～1284
[64] 张智明.非简并Raman耦合模型的改进型有效哈密顿量[J].量子光学学报,1996,2(1):32～36
[65] W.H.Louisell.Quantum statistical properties of radiation (Wiley, New York, 1973)
[66] Joshi A,Puri R R.Characteristics of Rabi oscillations in the two-mode squeezing state of the field.Phys.Rev.(A), 1990,42(7):4336～4348
[67] Puff R R,Agarwal G S.Finite-Q cavity electrodynamics:dynamical and statistical aspects [J].Phys.Rev.(A), 1987,35(8):3433～3442
[68] Brune M,Schmidt-Kaler F, Maali A etal.Quantum Rabi oscillation: a direct test of field quantization in a cavity [J].Phys.Rev.Lett., 1996,76(11): 1800～1804
[69] Joshi A,Puri R R. Dynamical evolution of the two-photo Jaynes-Cummings model in a Kerr-like medium [J].Phys.Rev.(A),1992, 45(7): 5056～5062
[70] Lei Xu,Zhi-Ming Zhang. Modified effective Hamiltonian for degenerate Raman process. Z.Phys.(B), 1994,B95(2):507～510
[71] Amitab H,Joshi A, Lawanda S V.Generalized Jaynes-Cummings model with a time-dependent atom-field couping [J].Phys.Rev.(A), 1993,48(3): 2276～2284
[72] 许静平,羊亚平.压缩态初始光场下变耦合系数的J-C模型[J].光学学报,2004,24(11):1577～1580
[73] 许静平,羊亚平.压缩态光场变耦合系数双光子J-C模型性质[J].光学学报,2005,25(2):251～255
[74] 朱小芹.耦合系数与时间有关的三能级原子同辐射场的相互作用[J].光学学报,1997,17(5):520～525
[75] 郭光灿.量子光学.北京:高等教育出版社,1990.227～227
[76] 罗耕贤,郭光灿.压缩态J-C模型中的崩塌—复原现象[J].光学学报,1990,10(1):1～5
[77] Agarwal G S.Field-correlation effects is multiphoton absorption process [J].Phys.Rev. (A), 1970,A1 (5): 1445～1459
[78] Joshi A, Lanwande S V.Effects of dipole interaction on the collapse-revival phenomenon of Rabi oscillations [J].Mod.Opt., 1991,38(5): 1407～1413
[79] 张立辉,李高翔,彭金生.位相损耗腔中简并双光子拉曼耦合系统中的熵特性[J].物理学报,2002,51(3):541～546