虚光子过程中的几何相位

doi:10.12677/MP.2017.74016

期刊菜单

虚光子过程中的几何相位
Geometric Phase in an Imaginary Photon Process

DOI: 10.12677/MP.2017.74016, PDF, HTML, XML, 被引量下载: 1,398 浏览: 4,370 科研立项经费支持
作者: 乔元新, 于肇贤：北京信息科技大学理学院，北京
关键词: 几何相位；推广的Jaynes-Cummings模型；Geometric Phase； Generalized Jaynes-Cummings Model

摘要: 利用Lewis-Riesenfeld不变量理论，研究了推广的含时二能级虚光子过程的 Jaynes-Cummings模型。发现周期情况下的几何相位与光子场的频率、光子和原子之间的耦合系数以及原子跃迁频率无关。

Abstract: By using the Lewis-Riesenfeld invariant theory, we have studied the geometric phase in a generalized time-dependent Jaynes-Cummings model with imaginary photon process for two-level atoms interacting with light field. It is found that the geometric phase in a cycle case has nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.

文章引用：乔元新, 于肇贤. 虚光子过程中的几何相位[J]. 现代物理, 2017, 7(4): 148-154. https://doi.org/10.12677/MP.2017.74016

参考文献

[1]	Pancharatnam, S. (1956) Generalized Theory of Interference, and Its Applications. Proceedings of the Indian Academy of Sciences—Section A, 44, 247-262.
[2]	Berry, M.V. (1984) Quantal Phase Factors Accompanying Adiabatic Changes. Proceedings of the Royal Society London, Series A, 392, 45. https://doi.org/10.1098/rspa.1984.0023
[3]	Aharonov, Y. and Anandan, J. (1987) Phase Change during a Cyclic Quantum Evolution. Physical Review Letters, 58, 1593. https://doi.org/10.1103/PhysRevLett.58.1593
[4]	Samuel, J. and Bhandari, R. (1988) General Setting for Berry’s Phase. Physical Review Letters, 60, 2339. https://doi.org/10.1103/PhysRevLett.60.2339
[5]	Mukunda, N. and Simon, R. (1933) Quantum Kinematic Approach to the Geometric Phase. I. General Formalism. Annals of Physics (N.Y.), 228, 205-268. https://doi.org/10.1006/aphy.1993.1093
[6]	Pati, A.K. (1995) Geometric Aspects of Noncyclic Quantum Evolutions. Physical Review A, 52, 2576. https://doi.org/10.1103/PhysRevA.52.2576
[7]	Uhlmann, A. (1986) Parallel Transport and “Quantum Holonomy” along Density Operators. Reports on Mathematical Physics, 24, 229-240. https://doi.org/10.1016/0034-4877(86)90055-8
[8]	Sjöqvist, E. (2000) Geometric Phases for Mixed States in Interferometry. Physical Review Letters, 85, 2845
[9]	Tong, D.M., et al. (2004) Kinematic Approach to the Mixed State Geometric Phase in Nonunitary Evolution. Physical Review Letters, 93, 080405. https://doi.org/10.1103/PhysRevLett.93.080405
[10]	Lewis, H.R. and Riesenfeld, W.B. (1969) An Exact Quantum Theory of the Time-Dependent Harmonic Oscillator and of a Charged Particle in a Time-Dependent Electromagnetic Field. Journal of Mathematical Physics, 10, 1458-1473. https://doi.org/10.1063/1.1664991
[11]	Gao, X.C., Xu, J.B. and Qian, T.Z. (1991) Geometric Phase and the Generalized Invariant Formulation. Physical Review A, 44, 7016. https://doi.org/10.1103/PhysRevA.44.7016
[12]	Gao, X.C., Fu, J. and Shen, J.Q. (2000) Quantum-Invariant Theory and the Evolution of a DIRAC FIELD in Friedmann-Robertson-Walker Flat Space-Times. European Journal of Physics, 13, 527-541. https://doi.org/10.1007/s100520000257
[13]	Gao, X.C., Gao, J., Qian, T.Z. and Xu, J.B. (1996) Quantum-Invariant Theory and the Evolution of a Quantum Scalar Field in Robertson-Walker Flat Spacetimes. Physical Review D, 53, 4374. https://doi.org/10.1103/PhysRevD.53.4374
[14]	Shen, J.Q. and Zhu, H.Y. (2003) arXiv: quant-ph/0305057v2
[15]	Richardson, D.J., et al. (1988) Demonstration of Berry's Phase Using Stored Ultracold Neutrons. Physical Review Letters, 61, 2030. https://doi.org/10.1103/PhysRevLett.61.2030
[16]	Wilczek, F. and Zee, A. (1984) Appearance of Gauge Structure in Simple Dynamical Systems. Physical Review Letters, 25, 2111. https://doi.org/10.1103/PhysRevLett.52.2111
[17]	Moody, J., et al. (1986) Realizations of Magnetic-Monopole Gauge Fields: Diatoms and Spin Precession. Physical Review Letters, 56, 893. https://doi.org/10.1103/PhysRevLett.56.893
[18]	Sun, C.P. (1990) Generalizing Born-Oppenheimer Approximations and Observable Effects of an Induced Gauge Field. Physical Review D, 41, 1349. https://doi.org/10.1103/PhysRevD.41.1349
[19]	Sun, C.P. (1993) Quantum Dynamical Model for Wave-Function Reduction in Classical and Macroscopic Limits. Physical Review A, 48, 898. https://doi.org/10.1103/PhysRevA.48.898
[20]	Sun, C.P. (1988) Flavor-Octet Dibaryons in the Quark Model. Physical Review D, 38, 298. https://doi.org/10.1103/PhysRevD.38.298
[21]	Sun, C.P., et al. (1988) High-Order Quantum Adiabatic Approximation and Berry's Phase Factor. Journal of Physics A, 21, 1595. https://doi.org/10.1088/0305-4470/21/7/023
[22]	Sun, C.P., et al. (2001) Quantum Measurement via Born-Oppenheimer Adiabatic Dynamics. Physical Review A, 63, Article ID: 012111. https://doi.org/10.1103/PhysRevA.63.012111
[23]	Chen, G., Li, J.Q. and Liang, J.Q. (2006) Critical Property of the Geometric Phase in the Dicke Model. Physical Review A, 74, Article ID: 054101. https://doi.org/10.1103/PhysRevA.74.054101
[24]	Chen, Z.D., Liang, J.Q., Shen, S.Q. and Xie, W.F. (2004) Dynamics and Berry Phase of Two-Species Bose-Einstein Condensates. Physical Review A, 69, Article ID: 023611. https://doi.org/10.1103/PhysRevA.69.023611
[25]	He, P.B., Sun, Q., Li, P., Shen, S.Q. and Liu, W.M. (2007) Magnetic Quantum Phase Transition of Cold Atoms in an Optical Lattice. Physical Review A, 76, Article ID: 043618. https://doi.org/10.1103/PhysRevA.76.043618
[26]	Li, Z.D., Li, Q.Y., Li, L. and Liu, W.M. (2007) Soliton Solution for the Spin Current in a Ferromagnetic Nanowire. Physical Review A, 76, Article ID: 026605. https://doi.org/10.1103/physreve.76.026605
[27]	Niu, Q., Wang, X.D., Kleinman, L., Liu, W.M., Nicholson, D.M.C. and Stocks, G.M. (1999) Adiabatic Dynamics of Local Spin Moments in Itinerant Magnets. Physical Review Letters, 83, 207. https://doi.org/10.1103/PhysRevLett.83.207
[28]	Jaynes, E.T. and Cummings, F.W. (1963) Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser. Proceedings of the IEEE, 51, 89-109. https://doi.org/10.1109/PROC.1963.1664
[29]	Huang, H.B. and Fan, H.Y. (1991) Jaynes-Cummings Model for Double m-Photon Lasers. Physics Letters A, 159, 323-327. https://doi.org/10.1016/0375-9601(91)90441-A
[30]	Fan, H.Y. and Li, L.S. (1996) Supersymmetric Unitary Operator for Some Generalized Jaynes-Cummings Models. Communications in Theoretical Physics, 25, 105. https://doi.org/10.1088/0253-6102/25/1/105
[31]	Wu, Y. and Yang, X. (1997) Jaynes-Cummings Model for a Trapped Ion in Any Position of a Standing Wave. Physical Review Letters, 78, 3086. https://doi.org/10.1103/PhysRevLett.78.3086
[32]	Wu, Y. (1996) Simple Algebraic Method to Solve a Coupled-Channel Cavity QED Model. Physical Review A, 54, 4534. https://doi.org/10.1103/PhysRevA.54.4534
[33]	Wu, Y., Yang, Y.X., Wu, Y. and Li, Y.J. (1997) Unified and Standardized Procedure to Solve Various Nonlinear Jaynes-Cummings Models. Physical Review A, 55, 4545.
[34]	Wei, J. and Norman, E. (1963) Lie Algebraic Solution of Linear Differential Equations. Journal of Mathematical Physics, 4, 575. https://doi.org/10.1063/1.1703993
[35]	Simon, B. (1983) Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase. Physical Review Letters, 51, 2167. https://doi.org/10.1103/PhysRevLett.51.2167

为你推荐

友情链接