Statistical approach to the Jaynes–Cummings model
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 116-123 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the dynamics of systems consisting of interacting two-level atoms and a field (microcavities). Such systems include the Jaynes–Cummings model. We formulate the problem and present a short history of it, derive a generalized kinetic equation for the system, find its solution, and show that this model allows describing photon emission and absorption.
Keywords: generalized kinetic equation, two-level atom, microcavity.
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N. N. Bogolyubov (Jr.); M. Yu. Rasulova; I. A. Tishabaev. Statistical approach to the Jaynes–Cummings model. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 116-123. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a9/

[1] Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett., 75:25 (1995), 4710–4613, arXiv: quant-ph/9511008 | DOI | MR | Zbl

[2] M. A. Nielssen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge, 2000 | MR

[3] E. T. Jaynes, F. W. Cummings, Proc. IEEE, 51:1 (1963), 89–109 | DOI

[4] H. I. Yoo, J. H. Eberly, Phys. Rep., 118:5 (1985), 239–337 | DOI

[5] B. W. Shore, P. L. Knight, J. Modern Opt., 40:7 (1993), 1195–1238 | DOI | MR | Zbl

[6] H. Weimer, G. Mahler, Phys. Rev. A, 76:5 (2007), 053819, 4 pp., arXiv: 0711.4705 | DOI

[7] S. De Liberato, D. Gerace, I. Carusotto, C. Ciuti, Phys. Rev. A, 80:5 (2009), 053810, 5 pp., arXiv: 0906.2706 | DOI

[8] G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett., 58:4 (1987), 353–356 | DOI

[9] M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, S. Haroche, Phys. Rev. Lett., 76:11 (1996), 1800–1803 | DOI | Zbl

[10] S. Bose, I. Fuentes-Guridi, P. L. Knight, V. Vedral, Phys. Rev. Lett., 87:5 (2001), 050401, 4 pp., arXiv: quant-ph/0103063 | DOI | MR

[11] S. Scheel, J. Eisert, P. L. Knight, M. B. Plenio, J. Modern Opt., 50:6–7 (2003), 881–889, arXiv: quant-ph/0207120 | DOI | MR | Zbl

[12] H. Azuma, J. Phys. D, 41:2 (2008), 025102, 10 pp., arXiv: quant-ph/0604086 | DOI

[13] N. N. Bogolyubov (ml.), B. I. Sadovnikov, A. S. Shumovskii, Matematicheskie metody statisticheskoi mekhaniki modelnykh sistem, Nauka, M., 1989 | MR | Zbl

[14] N. N. Bogolyubov, N. N. Bogolyubov (ml.), Aspekty teorii polyarona, Fizmatlit, M. | Zbl

[15] N. N. Bogolyubov (ml.), V. N. Plechko, A. S. Shumovskii, EChAYa, 14:6 (1983), 1483–1499

[16] N. N. Bogolyubov (ml.), Fam Le Kien, A. S. Shumovskii, TMF, 62:3 (1985), 461–471 | DOI | MR

[17] L. Allen, Dzh. Eberli, Opticheskii rezonans i dvukhurovnevye atomy, Mir, M., 1978

[18] A. O. Caldeira, A. J. Leggett, Annals Phys., 149:2 (1983), 374–456 | DOI

[19] U. Weiss, Quantum Dissipative Systems, Series in Modern Condensed Matter Physics, 10, World Sientific, Singapore, 1999 | DOI | Zbl

[20] H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems, Oxford Univ. Press, Oxford, 2002 | MR | Zbl

[21] A. E. Allahverdyan, R. Serral Gracià, M. Th. Nieuwenhuizen, Phys. Rev. E, 71:4 (2005), 046106, 22 pp., arXiv: quant-ph/0411018 | DOI | MR

[22] R. Zwanzig, Physica, 30:6 (1964), 1109–1123 | DOI | MR

[23] S. Nakajima, Progr. Theor. Phys., 20:6 (1958), 948–959 | DOI | MR | Zbl

[24] R. Zwanzig, J. Chem. Phys., 33:5 (1960), 1338–1341 | DOI | MR