A resummation formula for collapse and revival in the Jaynes-Cummings model

作者: Anatolii A Karatsuba , Ekatherina A Karatsuba

DOI: 10.1088/1751-8113/42/19/195304

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摘要: We present a new approach to the study of function atomic inversion in model interaction single two-level atom with mode quantized electromagnetic field coherent state an ideal resonator. The suggested is based on application certain number-theoretic results approximation trigonometric sums special form, particular functional equation Jacobi theta function. New asymptotic formulae for are found. asymptotics that we obtain make it possible predetermine details behavior various time intervals depending parameters system.

参考文章(18)
Anatolii A. Karatsuba, Ekatherina A. Karatsuba, Application of ATS in a Quantum-optical Model Birkhäuser Basel. pp. 211- 232 ,(2009) , 10.1007/978-3-7643-9906-1_13
E.T. Jaynes, F.W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser Proceedings of the IEEE. ,vol. 51, pp. 89- 109 ,(1963) , 10.1109/PROC.1963.1664
P Filipowicz, Quantum revivals in the Jaynes-Cummings model Journal of Physics A. ,vol. 19, pp. 3785- 3795 ,(1986) , 10.1088/0305-4470/19/18/024
A. A. Karatsuba, Approximation of exponential sums by shorter ones Proceedings of the Indian Academy of Sciences - Section A. ,vol. 97, pp. 167- 178 ,(1987) , 10.1007/BF02837821
Leonard Mandel, Emil Wolf, Optical Coherence and Quantum Optics ,(1995)
S. M. Chumakov, M. Kozierowski, J. J. Sanchez-Mondragon, Analytical approach to the photon statistics in the thermal Jaynes-Cummings model with an initially unexcited atom. Physical Review A. ,vol. 48, pp. 4594- 4597 ,(1993) , 10.1103/PHYSREVA.48.4594
Ekatherina A. Karatsuba, Approximation of sums of oscillating summands in certain physical problems Journal of Mathematical Physics. ,vol. 45, pp. 4310- 4321 ,(2004) , 10.1063/1.1797552
H I Yoo, J J Sanchez-Mondragon, J H Eberly, Non-linear dynamics of the fermion-boson model: interference between revivals and the transition to irregularity Journal of Physics A. ,vol. 14, pp. 1383- 1397 ,(1981) , 10.1088/0305-4470/14/6/015
N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Coherence versus incoherence: Collapse and revival in a simple quantum model Physical Review A. ,vol. 23, pp. 236- 247 ,(1981) , 10.1103/PHYSREVA.23.236
P. L. Knight, P. M. Radmore, Quantum origin of dephasing and revivals in the coherent-state Jaynes-Cummings model Physical Review A. ,vol. 26, pp. 676- 679 ,(1982) , 10.1103/PHYSREVA.26.676