Application of the Magnus and Fer expansions to a perturbative study of the time dependent Jaynes Cummings Model
DOI:
https://doi.org/10.24297/jap.v15i0.7965Keywords:
JCM, Matrix, Evolution, Operator, Perturbation, Ramp, Sweep, Wei-Norman, Feynman-Dyson, Magnus, Fer.Abstract
We apply the Magnus and Fer perturbation methods to Jaynes Cummings Model (JCM) with linear time dependence and show that the perturbation methods yield results which are appreciably close to the results obtained by Wei-Norman method, leading to exact solution when the Hamiltonian under consideration is an element of su(2), thus making the perturbation methods important for Hamiltonians for which a method of exact solution is not available.
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References
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[2] E.T. Jaynes and F. Cummings, Proc. of the IEEE, 51:89,1963.
[3] W. Wei and E. Norman, J. Math. Phys., 4(4):575,1963.
[4] P. Pechukas and J. C. Light, Journal of Chemical Physics, 44 : 3897, 1966.
[5] R. M. Wilcox, Journal of Mathematical Physics, 8(4 ): 962, 1967.
[6] T.V. Foerster, J. Phys. A : Math. Gen., 8(1):95,1975.
[7] J.H. Eberly, N.B. Narozhny and J.J. Sanchez-Mondragon, Phys. Rev. Lett., 44(20):1323, 1980.
[8] P.L. Knight and P.W. Milonni, Phys. Rep., 66(2):21-107,1980.
[9] H.I. Yoo, J.H. Eberly and J.J. Sanchez-Mondragon, J. Phys. A:Math.Gen., 14:1383,1981.
[10] N.B. Narozhny, J.J. Sanchez-Mondragon and J.H.Eberly, Phys. Rev. A, 23(1):236,1981.
[11] A. Bambini and P.R. Berman, Phys. Rev. A, 23(5):2496,1981.
[12] C. Riti and G. Vetri, Optics Comm., 44(2):105, 1982.
[13] P.L. Knignt and P.M. Radmore, Physics Letters, 90A(7):342,1982.
[14] S. Klarsfeld and J.A. Oteo, Division de Physique Théorique, IPN, F-91406 Orsay Cedex, France, 1989.
[15] A. Mufti, H. A. Schmitt and M. Sargent III, Americal Journal of Physics, 61 : 729, 1993.
[16] S. Yu, H. Rauch and Y.Zhang, Phys. Rev. A, 52(4):2585,1995.
[17] A. Dasgupta, J. Opt. B : Quantum and Semiclassical Optics, Volume 1, Number 1.
[18] M. Orszag, Quantum Optics, Springer.
[19] A. Dasgupta, Ph.D.Thesis, SINP, Kolkata.
[20] A.B. Klimov and S.M. Chumakov, A Group Theoretical Approach to Quantum Optics, Wiley-VCH.
[21] J.J. Sakurai, Advanced Quantum Mechanics, Second Edition, Addison-Wesley, 1999.
[22] M.Klaiber, D.Dimitrovsky and J.S.Briggs, Physical Review A, 79 : 043402, 2009.
[23] S.Blanes, F.Casas, J.A.Oteo and J.Ros, Physics Reports, 470 : 151-238, 2009.
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Published
2018-12-19
How to Cite
DAS, T. (2018). Application of the Magnus and Fer expansions to a perturbative study of the time dependent Jaynes Cummings Model. JOURNAL OF ADVANCES IN PHYSICS, 15, 5997–6017. https://doi.org/10.24297/jap.v15i0.7965
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