失谐Jaynes-Cummings模型中场与原子的量子特性
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摘要
首先，本文研究了相位损耗腔中大失谐下两个全同二能级原子与相干态场相互作用系统中场熵的演化特性。讨论了不同原子初始状态、光场平均光子数以及衰变常数对光场线性熵，原子线性熵和光场-原子系统线性熵的影响。结果表明，光场线性熵和原子线性熵较强地依赖于原子的初始状态，但系统的线性熵与原子的初始状态无关。当原子初始处于基态或激发态时，原子始终呈现纯态，而光场和原子-光场系统除在初始时刻对应着纯态外，在其它任何时刻均呈混合态。经一段时间以后，趋于一稳定值，到达稳定值的时间随衰变常数和初始平均光子数的增加而缩短。当原子初始处于基态与激发态的等概率相干叠加态时，系统的线性熵随时间的演化规律不变，光场线性熵随时间作振荡幅度减小的振荡，随时间的延长，该振荡消失，趋于与系统线性熵相同的稳定值。其振荡的时间随初始平均光子数的增加和衰变常数的增大而缩短。随着初始平均光子数的增加，光场的线性熵和系统的线性熵也随之而增大。原子线性熵随时间演化具有准周期性，并趋于一稳定值。随着光子数的增加，原子线性熵随时间的演化频率也随之而增大、振荡的幅度随之减小，原子线性熵与衰变常数无关。
其次，本文还研究了双模压缩真空场与∧型三能级原子非共振相互作用系统中场模失谐量δ和光场的初始压缩因子r对光场压缩影响。结果表明：光场呈现出较规则的压缩现象，压缩程度与r、δ明显相关。当r从零逐渐增大时，光场的压缩程度将经历一个由浅变深然后又由深变浅以至最终消失的过程：较小的场模失谐量对光场的压缩没有明显的影响，而较大的场模失谐量将加深光场的压缩程度。
By the quantum theory, we present the evolution of linear entropy in the phase-exhausting chamber, where two identical photons in the 2-level system interact with the coherent field under the condition of large disarrangement. We discuss the effect of different initial atomic status, the mean photon number and the decay constant on the photon linear entropy (PLE), the atom linear entropy (ALE) and the system photon-atom linear entropy (PALE). The results show that when the atom initially stays either in ground state or in the excited state the evolutions of the PLE and ALE are identical, but the PALE maintains zero. Besides, when the atom initially locates in the coherent state in which the probability of the ground state and excited one is equal, there are two points we want to mention. One is that when the mean photon number increases, the PALE evolution versus time is the same as the PLE and ALE ones. The other is that at the temperature of given value, the ALE is invariable while the time for PALE and PL
E to reach the stable value shortens as the decay constant X increases.
We also discuss the effect of Sand the initial compression factor r of optical field on the optical field compress. Here Sis the disarrangement value of the field variable pattern in the system, in which the non-resonant interaction takes place between double mode compression vacuum field and the A-form 3-level atom. The results shows that the optical field constricts regularly and the degree of the constriction strongly depends on the r and δ.
其次，本文还研究了双模压缩真空场与∧型三能级原子非共振相互作用系统中场模失谐量δ和光场的初始压缩因子r对光场压缩影响。结果表明：光场呈现出较规则的压缩现象，压缩程度与r、δ明显相关。当r从零逐渐增大时，光场的压缩程度将经历一个由浅变深然后又由深变浅以至最终消失的过程：较小的场模失谐量对光场的压缩没有明显的影响，而较大的场模失谐量将加深光场的压缩程度。
By the quantum theory, we present the evolution of linear entropy in the phase-exhausting chamber, where two identical photons in the 2-level system interact with the coherent field under the condition of large disarrangement. We discuss the effect of different initial atomic status, the mean photon number and the decay constant on the photon linear entropy (PLE), the atom linear entropy (ALE) and the system photon-atom linear entropy (PALE). The results show that when the atom initially stays either in ground state or in the excited state the evolutions of the PLE and ALE are identical, but the PALE maintains zero. Besides, when the atom initially locates in the coherent state in which the probability of the ground state and excited one is equal, there are two points we want to mention. One is that when the mean photon number increases, the PALE evolution versus time is the same as the PLE and ALE ones. The other is that at the temperature of given value, the ALE is invariable while the time for PALE and PL
E to reach the stable value shortens as the decay constant X increases.
We also discuss the effect of Sand the initial compression factor r of optical field on the optical field compress. Here Sis the disarrangement value of the field variable pattern in the system, in which the non-resonant interaction takes place between double mode compression vacuum field and the A-form 3-level atom. The results shows that the optical field constricts regularly and the degree of the constriction strongly depends on the r and δ.
引文
[1] E. T. Jaynes, F. W. Cummings. Comparison of quantum and semi classical radiation pheories with application to the beam maser Proc, IEEE. 1963,51(1):89～109.
[2] Zhou P, Hu Z L, Peng J S. Effect of atomic coherence on the collapses and revivals in some generalized Janyes-Cummings models. J. Mod. Opt.,1992,39(1):49～62.
[3] 李高翔，彭金生．论Jaynes-Cummings模型中原子偶极压缩和光场压缩间的关联 物理学报，1995，44(10)：1670～1678．
[4] 李高翔．彭金生．火谐量对双光子J-C模型中光场位相扩散及频率漂移的影响．光学学报，1993，13(2)：120～124．
[5] Li G X, Peng J S. Influences of ac Stark shifts on coherent population trapping in the atom-field coupling system via Raman two-photon processes. Phys. Rev. (A), 1995,52(1):465～471.
[6] G. Compagno, J. S. Peng, F. Persico, Squeezing in a two-photon Dicke hamiltonian Opt. Commun.,1986,57(6)415～417.
[7] S. Y. Zhu, Non-classical features in the three-level Jaynes-Cummings model. J. Mod. Opt.,1989,36(4):499～513.
[8] V. Buzek, Light squeezing in the two-photon Jaynes-Cummings model:far-off-resonant limit. Phys. Lett. (A),151A(5):234～240.
[9] G. Rempe, H. Walther, N. Klein, Observation of quantum collapse and revival in a one-atom maser phys. Rev. Lett, 1987,58: 353～360.
[10] Phoenis S J D, Kinght P L. Fluctuations and entropy in models of quantum optical resonance. Ann. Phys.,1988,186(2):381～407.
[11] S M Barnett, S J D Phoenix. Entropy as a measure of quantum optical correlation Phys, Rev, A, 1989,,40(5):2404～2409.
[12] Phoenis S J D, Kinght P L. Periodicity, phase and entropy in models of two-photon resonance. J. Opt. Soc. Am. (B),1990,7(1):116～124.
[13] 万琳，刘三秋，陶向阳，虚光子过程对“两个二能级原子-单模光场”相互作用系统场熵演化特性的影响，光子学报，2001 30(6)：651．
[14] 黄燕霞．郝东山，汪毅，Kerr效应对非线性Jaynes-Cummings模型场熵和缠结的影响，光子学报，2002 31 (12)：1448．
[15] 李永平，柳永亮，贺金玉，双光子J-C模型场熵的压缩特性．量子光学学报，2003 9(3)．
[16] Fang Maofa. Evolution of field entropy in the intensity-dependent coupling J-C model. Acta Optica Sinica, 1995,15(3):296～300.
[17] Huang Y X, Guo G C. Poroperties of the field entropy evolution in the Jayness-Cummings model with initial squeezed vacuum. Acta Sinica Quantum Optica, 1996,2(6):97～104.
[18] Orvlowski A, paul H, Kastelewicj G. Dynamical properties of a classical-like entropy in the Jaynes-Cummings model. Phys. Rev. (A), 1995,52(2):1621～1628.
[19] 方卯发，周鹏．多光子Jaynes-Cummings模型场熵的演化，光学学报 1993 13(9)：799～804．
[20] 方卯发，刘惠恩，附加克尔介质J-C模型场熵的演化，光学学报，1994，14(5)：475～579．
[21] Peixoto de Faria J G, Nemes M C. Dissipative dynamics of the Jaynes-Cummings model in the dispersive approximation:Analytical results. Phys. Rev. (A), 1999,59(5):3918～3925.
[22] Zurek W H, Habib S, Paz J P Coherent states via decoherence Phys. Rev. Lett.,1993,70(9):1187～1190.
[23] 张立辉，李高翔，彭金生．相位损耗腔中大失谐Jaynes-Cummings模型中熵的演化．光学学报，2002，22(8)：907～911．
[24] Walls DF, Milburn GJ. Effect of dissipation on quantum coherence. Phys. Rev. (A),1985,31(4):2403～2408.
[25] Hiroshima T. Oecoherence and entanglement in two-ode squeezed vacuum states Phys. Rev. 2001,63(2):022305-1～022305-4.
[26] D. F. Walls, P. Zollor, Peduced quantum fluctuations in resonance fluorescence. Phys. Rev. Lett.,1981,47(10):709～711.
[27] 刘三秋，万琳，刘素梅，克尔介质中“耦合双原子-场”模型的光场压缩效应．光学学报，2002 22(8)：902．
[28] 田永红，彭金生．双模压缩真空场作用下二能级原子的偶极压缩与相干俘获[J]．
物理学报，1999，48(11)：2060～2069．
[29] 黄春佳、周明、厉江帆，孔凡志，双模压缩真空场与耦合双原子相互作用中光场的量子特性[J]．物理学报，2000，49(11)：2159～2163．
[30] 田永红、徐大海，彭金生．级联二能级原子的偶极振幅平方压缩[J]．量子电子学报．2001，18(4)：334～339．
[31] 陶向阳，刘金明，刘三秋，傅传鸿，Kerr介质中三能级原子与双模场非共振相互作用的量子统计性质，物理学报，2000，49(8)：1464～1470．
[32] 谢芳森．刘小青，陈明玉，与A型三能级原子非共振相互作用的SU(1，1)场的性质．光子学报，2002，31(12)：1439．
[33] C. E. Shannon, W. Weaver, The mathematical theory of communication. Illini Books Urbana, Ⅱ,1963.
[34] 彭金生，李高翔．近代量子光学导论，北京：科学出版社(1996)．
[35] Walls D F, Milburn G J. Effect of dissipation on quantum coherence. Phys. Rev. (A), 1985,31(4):2403～2408.
[2] Zhou P, Hu Z L, Peng J S. Effect of atomic coherence on the collapses and revivals in some generalized Janyes-Cummings models. J. Mod. Opt.,1992,39(1):49～62.
[3] 李高翔，彭金生．论Jaynes-Cummings模型中原子偶极压缩和光场压缩间的关联 物理学报，1995，44(10)：1670～1678．
[4] 李高翔．彭金生．火谐量对双光子J-C模型中光场位相扩散及频率漂移的影响．光学学报，1993，13(2)：120～124．
[5] Li G X, Peng J S. Influences of ac Stark shifts on coherent population trapping in the atom-field coupling system via Raman two-photon processes. Phys. Rev. (A), 1995,52(1):465～471.
[6] G. Compagno, J. S. Peng, F. Persico, Squeezing in a two-photon Dicke hamiltonian Opt. Commun.,1986,57(6)415～417.
[7] S. Y. Zhu, Non-classical features in the three-level Jaynes-Cummings model. J. Mod. Opt.,1989,36(4):499～513.
[8] V. Buzek, Light squeezing in the two-photon Jaynes-Cummings model:far-off-resonant limit. Phys. Lett. (A),151A(5):234～240.
[9] G. Rempe, H. Walther, N. Klein, Observation of quantum collapse and revival in a one-atom maser phys. Rev. Lett, 1987,58: 353～360.
[10] Phoenis S J D, Kinght P L. Fluctuations and entropy in models of quantum optical resonance. Ann. Phys.,1988,186(2):381～407.
[11] S M Barnett, S J D Phoenix. Entropy as a measure of quantum optical correlation Phys, Rev, A, 1989,,40(5):2404～2409.
[12] Phoenis S J D, Kinght P L. Periodicity, phase and entropy in models of two-photon resonance. J. Opt. Soc. Am. (B),1990,7(1):116～124.
[13] 万琳，刘三秋，陶向阳，虚光子过程对“两个二能级原子-单模光场”相互作用系统场熵演化特性的影响，光子学报，2001 30(6)：651．
[14] 黄燕霞．郝东山，汪毅，Kerr效应对非线性Jaynes-Cummings模型场熵和缠结的影响，光子学报，2002 31 (12)：1448．
[15] 李永平，柳永亮，贺金玉，双光子J-C模型场熵的压缩特性．量子光学学报，2003 9(3)．
[16] Fang Maofa. Evolution of field entropy in the intensity-dependent coupling J-C model. Acta Optica Sinica, 1995,15(3):296～300.
[17] Huang Y X, Guo G C. Poroperties of the field entropy evolution in the Jayness-Cummings model with initial squeezed vacuum. Acta Sinica Quantum Optica, 1996,2(6):97～104.
[18] Orvlowski A, paul H, Kastelewicj G. Dynamical properties of a classical-like entropy in the Jaynes-Cummings model. Phys. Rev. (A), 1995,52(2):1621～1628.
[19] 方卯发，周鹏．多光子Jaynes-Cummings模型场熵的演化，光学学报 1993 13(9)：799～804．
[20] 方卯发，刘惠恩，附加克尔介质J-C模型场熵的演化，光学学报，1994，14(5)：475～579．
[21] Peixoto de Faria J G, Nemes M C. Dissipative dynamics of the Jaynes-Cummings model in the dispersive approximation:Analytical results. Phys. Rev. (A), 1999,59(5):3918～3925.
[22] Zurek W H, Habib S, Paz J P Coherent states via decoherence Phys. Rev. Lett.,1993,70(9):1187～1190.
[23] 张立辉，李高翔，彭金生．相位损耗腔中大失谐Jaynes-Cummings模型中熵的演化．光学学报，2002，22(8)：907～911．
[24] Walls DF, Milburn GJ. Effect of dissipation on quantum coherence. Phys. Rev. (A),1985,31(4):2403～2408.
[25] Hiroshima T. Oecoherence and entanglement in two-ode squeezed vacuum states Phys. Rev. 2001,63(2):022305-1～022305-4.
[26] D. F. Walls, P. Zollor, Peduced quantum fluctuations in resonance fluorescence. Phys. Rev. Lett.,1981,47(10):709～711.
[27] 刘三秋，万琳，刘素梅，克尔介质中“耦合双原子-场”模型的光场压缩效应．光学学报，2002 22(8)：902．
[28] 田永红，彭金生．双模压缩真空场作用下二能级原子的偶极压缩与相干俘获[J]．
物理学报，1999，48(11)：2060～2069．
[29] 黄春佳、周明、厉江帆，孔凡志，双模压缩真空场与耦合双原子相互作用中光场的量子特性[J]．物理学报，2000，49(11)：2159～2163．
[30] 田永红、徐大海，彭金生．级联二能级原子的偶极振幅平方压缩[J]．量子电子学报．2001，18(4)：334～339．
[31] 陶向阳，刘金明，刘三秋，傅传鸿，Kerr介质中三能级原子与双模场非共振相互作用的量子统计性质，物理学报，2000，49(8)：1464～1470．
[32] 谢芳森．刘小青，陈明玉，与A型三能级原子非共振相互作用的SU(1，1)场的性质．光子学报，2002，31(12)：1439．
[33] C. E. Shannon, W. Weaver, The mathematical theory of communication. Illini Books Urbana, Ⅱ,1963.
[34] 彭金生，李高翔．近代量子光学导论，北京：科学出版社(1996)．
[35] Walls D F, Milburn G J. Effect of dissipation on quantum coherence. Phys. Rev. (A), 1985,31(4):2403～2408.