原子与双模纠缠光场相互作用的场熵演化特性
|
摘要
自从描述原子与多模辐射场相互作用的狄克(Dicke)模式,以及描述单模光场与一个二能级原子相互作用的Jaynes-Cummings模型提出以来,人们据此对原子与光场相互作用系统所呈现出的非经典特性进行了了解和探讨,并对Jaynes-Cummings模型进行了多种形式的拓展。Phoenix和Knight( P- K)将熵理论应用于量子光学领域,根据P-K量子熵理论,在光场-原子相互作用系统中,光场(原子)熵演化行为反映了光场与原子关联程度的演化特性,熵越高关联就越强。Buzek和Jex最先将描述二能级原子和光场相互作用的Jaynes-Cummings模型与Kerr介质结合,提出了原子周围存在非线性介质的B-J模型,并研究了该模型动力学行为。随后的研究发现Kerr介质的存在使原子布局反转更有规律,光场亚泊松分布、双模场非经典相关度以及场熵演化规律皆因Kerr效应而有规律变化。Kerr效应的非线性对原子与光场的量子特性的影响,已经引起人们广泛的关注。
本文首先简要介绍熵的统计定义,以及熵的量子光学引入;其次介绍前人关于原子-单模光场相互作用系统的熵演化特性,以及原子-双模光场相互作用系统的熵演化特性;论文第三部分,分别计算在无介质和有kerr介质的非线性条件下,原子与双模纠缠光场相互作用系统的场熵演化规律。
Since the description of a atom with the multi-mold radiation field of Dicke the (Dicke) model, as well as the description of single model optical field the Jaynes-Cummings model which has affected mutually with a two energy level atom proposes, according to the above , mutually affected the non-classical characteristic to the atom and the optical field of the system presented to carry on the understanding and the discussion, and has carried on many kinds of form development to the Jaynes-Cummings model. Phoenix and Knight (P- K) apply the entropy theory in the quantum optics domain, according to P-K quantum entropy theory, affection in the mutual system of the optical field– atom, the entropy evolution of the optical field (atom) had reflected the optical field and the atomic connection degree of evolved characteristic, the entropy is higher and the connection is stronger. Buzek and Jex described the Jaynes-Cummings model, which two energy level atoms and the optical field affect mutually, and take together with the Kerr medium ,then proposed that around the atom has the non-linear medium named the B-J model. And has studied this model dynamics behavior. Afterwards research discovered that the existence of the Kerr medium causes the atomic changes more orderly. Optical field Asia Poisson's distribution, non-classical degree of correlation in the double model field and field entropy evolution get weaker when the Kerr effect get weaker. The influence in non-linearity of Kerr effect to atomic and optical field quantum characteristic, has already aroused the people widespread interest.
This article first is brief introduces the statistical definition of the entropy, as well as the introduction about entropy to the quantum optics. Next, introduced other workers` work about the atomic - single model optical field mutually in the entropy characteristic; as well as the atomic - double model optical field affects the system mutually the entropy characteristic.In the third part of the paper, calculates separately in having the non-medium and having the kerr medium non-linear condition, atomic and the double model entanglement optical field affects the system mutually the rule of the field entropy evolution.
本文首先简要介绍熵的统计定义,以及熵的量子光学引入;其次介绍前人关于原子-单模光场相互作用系统的熵演化特性,以及原子-双模光场相互作用系统的熵演化特性;论文第三部分,分别计算在无介质和有kerr介质的非线性条件下,原子与双模纠缠光场相互作用系统的场熵演化规律。
Since the description of a atom with the multi-mold radiation field of Dicke the (Dicke) model, as well as the description of single model optical field the Jaynes-Cummings model which has affected mutually with a two energy level atom proposes, according to the above , mutually affected the non-classical characteristic to the atom and the optical field of the system presented to carry on the understanding and the discussion, and has carried on many kinds of form development to the Jaynes-Cummings model. Phoenix and Knight (P- K) apply the entropy theory in the quantum optics domain, according to P-K quantum entropy theory, affection in the mutual system of the optical field– atom, the entropy evolution of the optical field (atom) had reflected the optical field and the atomic connection degree of evolved characteristic, the entropy is higher and the connection is stronger. Buzek and Jex described the Jaynes-Cummings model, which two energy level atoms and the optical field affect mutually, and take together with the Kerr medium ,then proposed that around the atom has the non-linear medium named the B-J model. And has studied this model dynamics behavior. Afterwards research discovered that the existence of the Kerr medium causes the atomic changes more orderly. Optical field Asia Poisson's distribution, non-classical degree of correlation in the double model field and field entropy evolution get weaker when the Kerr effect get weaker. The influence in non-linearity of Kerr effect to atomic and optical field quantum characteristic, has already aroused the people widespread interest.
This article first is brief introduces the statistical definition of the entropy, as well as the introduction about entropy to the quantum optics. Next, introduced other workers` work about the atomic - single model optical field mutually in the entropy characteristic; as well as the atomic - double model optical field affects the system mutually the entropy characteristic.In the third part of the paper, calculates separately in having the non-medium and having the kerr medium non-linear condition, atomic and the double model entanglement optical field affects the system mutually the rule of the field entropy evolution.
引文
① 北京大学物理系《量子统计物理学》编写组 《量子统计物理学》
②彭金生 ,李高翔 ,《近代量子光学导论》
③王建伟 相干光场与二能级原子的相互作用及场熵演化[J] 新疆大学学报 (理工版)2001,Vol 18 49
④黄燕霞, 郭光灿 ,压缩真空态 Jaynes-Cummings 模型中场熵的演化特性, 量子光学学报 1996,2(2),97
⑤宋军,沈金玲,张刚,曹卓良,两纠缠原子与光场相互作用系统场熵演化特性[J].原子与分子物理学报 2006,Vol.23 No.4 ,Aug.
⑥郑小虎, 曹卓良 , 双模纠缠光场与二能级原子相互作用的特性[J] 光电子技术与信息 2004,17(6),26
⑦ 林继成,郑小虎,曹卓良 kerr 介质中双模纠缠相干光与 Bell 态原子相互作用系统原子偶极压缩 物理学报 [J] 2007,Vol.56.No.2 837
[1] C.E.Shannon and W.Weaver ,The Mathematical Theory of Communicaiion ,Urbana ,Ill.:University of Illinois Press ,1949
[2] E.T.Jaynes, Phys. Rev. , 1957,106, 620
[3] E.T.Jaynes, Phys. Rev. , 1957,108, 171
[4] R.C.Tolman, The Principles of Statistical Mechanics, Oxford: Clarendon, 1938
[5] Phoenix S J D, Knight P L. Fluctuations and entropy in models of quantum optical resonance. Ann. Phys., 1998, 186,381
[6] Barnett S M, Phoenix S J D. Entropy as measure of quantum optical correlation. Phys. Rev. A, 1989, 40,2404
[7] Araki H. Lieb E Commun. Math. Phys. 1970,18 ,160
[8] Gamma H. Matrix treatment of partial coherence [M]. Progress in ptics, 1964, III,189
[9] Einsten A, Podolsky B, Rosen N. Phys. Rev. ,1935, 47,777
[10] Peres A . Phys. Rev. Lett. , 1996,77,1413
[11] 彭金生 ,李高翔 ,《近代量子光学导论》科学出版社 [M].
[12] 王建伟 相干光场与二能级原子的相互作用及场熵演化[J]. 新疆大学学报 (理工版)2001,Vol 18 49
[13] 于祖荣 量子光学中的非经典态[J] 物理进展 1999,3(1),77
[14] 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
[15] S.J.D.Phoenix ,P.L.Knight. Fluctuations and entropy in models of quantum optiona resonance . Ann, Phys.(N.Y.),1988, 186,381
[16] 黄燕霞, 郭光灿 ,压缩真空态 Jaynes-Cummings 模型中场熵的演化特性[J].量子光学学报 1996,2(2),97
[17] H.P.Yuen , Two-photon coherent states of the radiation field Phys. Rev. (A) 1976, 13(6),2226
[18] Bennett C H ,DiVincenzo D P , Smolin J A et al Phys. Rev.A 1996 ,54 ,3824
[19] Song J ,Cao Z L. Quantum properties of light of two identical two-level entangled atoms interacting with coherent state[J] .J.At.Mol.Phys.,2004,22,153 (in China)
[20] Song J ,Cao Z L. Dynamical properties in the system of coherent state[J].J.At.Mol.Phys.,2004,21,446 (in China)
[21] 郑小虎, 曹卓良 , 双模纠缠光场与二能级原子相互作用的特性[J]. 光电子技术与信息 2004,17(6) :26
[22] Liu T K, Peng J S Acta Opt. Sin. 1997 ,17,991(in Chinese)
[23] Song J ,Cao Z L Acta Phys. Sin. 2005,54,696 (in Chinese)
[24] R. H. Dicke, Phus.Rev. , 1954,93,99
[25] C. Leonardi. F. Persico and G. Veti, Dicke model and theory of driven and spontaneous emission, La Rivista de Nuovo Cimento, 1986.
[26] 陈本藜, 曾民勇 《量子力学中的谐振子》 福建科学技术出版社 [M].
[27] R. Loudon, The Quantum Theory of Light , 2nd ed. ,Clarendon,1983.
[28] M.Born and E. Wolf. Principles of Optics, 2nd ed. ,Perganmon ,1964
[29] A. Ovlowki, H. Paul. G. Kastelewicz. Dynamical Properities of a classical-like entropy in the Jaynes-Cummings model. Phys. Rev. (A),1995,52(2),1621
[30] 黄春佳,贺慧勇,周明, 方家元,黄祖洪, 光场与纠缠双原子相互作用过程中的熵演化特性 物理学报 2006,V. 55. N0.4, April, 1764
[31] C. H. Bennett, D. P. Divincenzo, J. Smolin, W. K. Wootters. Mixed-state entanglement and quantum error correction [J]. Phys. Rev.,1996, 54,3824.
[32] A. Ekerrt, R. Jozsa. Quantum computation and Shor’s factoring algorithm [J]. Rev. Mod. Phys,1996,68,73.
[33] C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wotters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev. Lett., 1993,70,1895.
[34] C. H. Bennett,S. J. Wiesner. Communication via one and two-particle operaters on Einstein-Podosky-Rosen stares. [J]. Phys. Rev. Lett.,1992,69,2881.
[35] 查新未 量子纯态纠缠态的构成与纠缠度[J].西安邮电学院学报,2000,49(5),825
[36] Walls D F, Zoller P. Reduced quantum fluctuations in resonance fluorescence [J]. Phys Rev Lett.1981,47,709
[37] Lai W K, Buek V, Knight P L. Dynamics of a three-level atom in a two-mode squeezed vacuum[J]. Phys Rev (A), 1991, 44,6043
[38] Einstein A, Podolsky B, Rosen N, Phys. Rev. 1935 ,47,777
[39] Schro && doinger E. Die gegenwartige situation in derquantenme chanik[J]. Naturwissenschaften, 1935, 23,807, 823, 844
[40] 宋军,沈金玲,张刚,曹卓良,两纠缠原子与光场相互作用系统场熵演化特性[J].原子与分子物理学报 2006,Vol.23 No.4 Aug.
[41] 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, Nov.Vol 43, No.11, 1776
[42] 林继成,郑小虎,曹卓良 kerr 介质中双模纠缠相干光与 Bell 态原子相互作用系统原子偶极压缩 [J]. 物理学报 2007,Vol.56.No.2 837
[43] 刘堂昆,彭金生, 类克尔介质中原子布局数的演化和偶极压缩效应 [J]. 光学学报1997, 17,991
[44] 宋军,曹卓良, 两纠缠原子与二项式光场相互作用的动力学 [J]. 物理学报 2005,54,696
②彭金生 ,李高翔 ,《近代量子光学导论》
③王建伟 相干光场与二能级原子的相互作用及场熵演化[J] 新疆大学学报 (理工版)2001,Vol 18 49
④黄燕霞, 郭光灿 ,压缩真空态 Jaynes-Cummings 模型中场熵的演化特性, 量子光学学报 1996,2(2),97
⑤宋军,沈金玲,张刚,曹卓良,两纠缠原子与光场相互作用系统场熵演化特性[J].原子与分子物理学报 2006,Vol.23 No.4 ,Aug.
⑥郑小虎, 曹卓良 , 双模纠缠光场与二能级原子相互作用的特性[J] 光电子技术与信息 2004,17(6),26
⑦ 林继成,郑小虎,曹卓良 kerr 介质中双模纠缠相干光与 Bell 态原子相互作用系统原子偶极压缩 物理学报 [J] 2007,Vol.56.No.2 837
[1] C.E.Shannon and W.Weaver ,The Mathematical Theory of Communicaiion ,Urbana ,Ill.:University of Illinois Press ,1949
[2] E.T.Jaynes, Phys. Rev. , 1957,106, 620
[3] E.T.Jaynes, Phys. Rev. , 1957,108, 171
[4] R.C.Tolman, The Principles of Statistical Mechanics, Oxford: Clarendon, 1938
[5] Phoenix S J D, Knight P L. Fluctuations and entropy in models of quantum optical resonance. Ann. Phys., 1998, 186,381
[6] Barnett S M, Phoenix S J D. Entropy as measure of quantum optical correlation. Phys. Rev. A, 1989, 40,2404
[7] Araki H. Lieb E Commun. Math. Phys. 1970,18 ,160
[8] Gamma H. Matrix treatment of partial coherence [M]. Progress in ptics, 1964, III,189
[9] Einsten A, Podolsky B, Rosen N. Phys. Rev. ,1935, 47,777
[10] Peres A . Phys. Rev. Lett. , 1996,77,1413
[11] 彭金生 ,李高翔 ,《近代量子光学导论》科学出版社 [M].
[12] 王建伟 相干光场与二能级原子的相互作用及场熵演化[J]. 新疆大学学报 (理工版)2001,Vol 18 49
[13] 于祖荣 量子光学中的非经典态[J] 物理进展 1999,3(1),77
[14] 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
[15] S.J.D.Phoenix ,P.L.Knight. Fluctuations and entropy in models of quantum optiona resonance . Ann, Phys.(N.Y.),1988, 186,381
[16] 黄燕霞, 郭光灿 ,压缩真空态 Jaynes-Cummings 模型中场熵的演化特性[J].量子光学学报 1996,2(2),97
[17] H.P.Yuen , Two-photon coherent states of the radiation field Phys. Rev. (A) 1976, 13(6),2226
[18] Bennett C H ,DiVincenzo D P , Smolin J A et al Phys. Rev.A 1996 ,54 ,3824
[19] Song J ,Cao Z L. Quantum properties of light of two identical two-level entangled atoms interacting with coherent state[J] .J.At.Mol.Phys.,2004,22,153 (in China)
[20] Song J ,Cao Z L. Dynamical properties in the system of coherent state[J].J.At.Mol.Phys.,2004,21,446 (in China)
[21] 郑小虎, 曹卓良 , 双模纠缠光场与二能级原子相互作用的特性[J]. 光电子技术与信息 2004,17(6) :26
[22] Liu T K, Peng J S Acta Opt. Sin. 1997 ,17,991(in Chinese)
[23] Song J ,Cao Z L Acta Phys. Sin. 2005,54,696 (in Chinese)
[24] R. H. Dicke, Phus.Rev. , 1954,93,99
[25] C. Leonardi. F. Persico and G. Veti, Dicke model and theory of driven and spontaneous emission, La Rivista de Nuovo Cimento, 1986.
[26] 陈本藜, 曾民勇 《量子力学中的谐振子》 福建科学技术出版社 [M].
[27] R. Loudon, The Quantum Theory of Light , 2nd ed. ,Clarendon,1983.
[28] M.Born and E. Wolf. Principles of Optics, 2nd ed. ,Perganmon ,1964
[29] A. Ovlowki, H. Paul. G. Kastelewicz. Dynamical Properities of a classical-like entropy in the Jaynes-Cummings model. Phys. Rev. (A),1995,52(2),1621
[30] 黄春佳,贺慧勇,周明, 方家元,黄祖洪, 光场与纠缠双原子相互作用过程中的熵演化特性 物理学报 2006,V. 55. N0.4, April, 1764
[31] C. H. Bennett, D. P. Divincenzo, J. Smolin, W. K. Wootters. Mixed-state entanglement and quantum error correction [J]. Phys. Rev.,1996, 54,3824.
[32] A. Ekerrt, R. Jozsa. Quantum computation and Shor’s factoring algorithm [J]. Rev. Mod. Phys,1996,68,73.
[33] C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wotters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev. Lett., 1993,70,1895.
[34] C. H. Bennett,S. J. Wiesner. Communication via one and two-particle operaters on Einstein-Podosky-Rosen stares. [J]. Phys. Rev. Lett.,1992,69,2881.
[35] 查新未 量子纯态纠缠态的构成与纠缠度[J].西安邮电学院学报,2000,49(5),825
[36] Walls D F, Zoller P. Reduced quantum fluctuations in resonance fluorescence [J]. Phys Rev Lett.1981,47,709
[37] Lai W K, Buek V, Knight P L. Dynamics of a three-level atom in a two-mode squeezed vacuum[J]. Phys Rev (A), 1991, 44,6043
[38] Einstein A, Podolsky B, Rosen N, Phys. Rev. 1935 ,47,777
[39] Schro && doinger E. Die gegenwartige situation in derquantenme chanik[J]. Naturwissenschaften, 1935, 23,807, 823, 844
[40] 宋军,沈金玲,张刚,曹卓良,两纠缠原子与光场相互作用系统场熵演化特性[J].原子与分子物理学报 2006,Vol.23 No.4 Aug.
[41] 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, Nov.Vol 43, No.11, 1776
[42] 林继成,郑小虎,曹卓良 kerr 介质中双模纠缠相干光与 Bell 态原子相互作用系统原子偶极压缩 [J]. 物理学报 2007,Vol.56.No.2 837
[43] 刘堂昆,彭金生, 类克尔介质中原子布局数的演化和偶极压缩效应 [J]. 光学学报1997, 17,991
[44] 宋军,曹卓良, 两纠缠原子与二项式光场相互作用的动力学 [J]. 物理学报 2005,54,696
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |