Abstract
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.
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Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett., 75, 4710–4613 (1995); arXiv:quant-ph/9511008v1 (1995).
M. A. Nielssen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge (2000).
E. T. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89–109 (1963).
H. I. Yoo and J. H. Eberly, Phys. Rep., 118, 239–337 (1985).
B. W. Shore and P. L. Knight, J. Modern Opt., 40, 1195–1238 (1993).
H. Weimer and G. Mahler, Phys. Rev. A, 76, 053819 (2007); arXiv:0711.4705v1 [quant-ph] (2007).
S. De Liberato, D. Gerace, I. Carusotto, and C. Ciuti, Phys. Rev. A, 80, 053810 (2009); arXiv:0906.2706v1 [quant-ph] (2009).
G. Rempe, H. Walther, and N. Klein, Phys. Rev. Lett., 58, 353–356 (1987).
M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, Phys. Rev. Lett., 76, 1800–1803 (1996).
S. Bose, I. Fuentes-Guridi, P. L. Knight, and V. Vedral, Phys. Rev. Lett., 87, 050401 (2001); arXiv:quant-ph/0103063v2 (2001).
S. Scheel, J. Eisert, P. L. Knight, and M. B. Plenio, J. Modern Opt., 50, 881–889 (2003); arXiv:quant-ph/0207120v1 (2002).
H. Azuma, J. Phys. D, 41, 025102 (2008); arXiv:quant-ph/0604086v6 (2006).
N. N. Bogolyubov Jr., B. I. Sadovnikov, and A. S. Shumovskii, Mathematical Methods in the Statistical Mechanics of Model Systems [in Russian], Nauka, Moscow (1989).
N. N. Bogoliubov and N. N. Bogolyubov Jr., Aspects of Polaron Theory [in Russian], Fizmatlit, Moscow (2004).
N. N. Bogolyubov Jr., V. N. Plechko, and A. S. Shumovsky, Phys. Part. Nucl., 14, 1483–1499 (1983).
N. N. Bogolyubov, F. L. Kien, and A. S. Shumovskii, Theor. Math. Phys., 62, 308–316 (1985).
L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, Wiley, New York (1975).
A. O. Caldeira and A. J. Leggett, Annals Phys., 149, 374–456 (1983).
U. Weiss, Quantum Dissipative Systems (Ser. Mod. Cond. Mat. Phys., Vol. 10), World Scientific, Singapore (1999).
H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford Univ. Press, Oxford (2002).
A. E. Allahverdyan, R. Serral Gracià, and M. T. Nieuwenhuizen, Phys. Rev. E, 71, 046106 (2005); arXiv:quantph/0411018v1 (2004).
R. Zwanzig, Phys., 30, 1109–1123 (1964).
S. Nakajima, Progr. Theoret. Phys., 20, 948–959 (1958).
R. Zwanzig, J. Chem. Phys., 33, 1338–1341 (1960).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 171, No. 1, pp. 116–123, April, 2012.
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Bogolyubov, N.N., Rasulova, M.Y. & Tishabaev, I.A. Statistical approach to the Jaynes-Cummings model. Theor Math Phys 171, 523–530 (2012). https://doi.org/10.1007/s11232-012-0050-5
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DOI: https://doi.org/10.1007/s11232-012-0050-5