Skip to main content
Log in

Statistical approach to the Jaynes-Cummings model

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 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).

    Article  MathSciNet  ADS  Google Scholar 

  2. M. A. Nielssen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge (2000).

    Google Scholar 

  3. E. T. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89–109 (1963).

    Article  Google Scholar 

  4. H. I. Yoo and J. H. Eberly, Phys. Rep., 118, 239–337 (1985).

    Article  ADS  Google Scholar 

  5. B. W. Shore and P. L. Knight, J. Modern Opt., 40, 1195–1238 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. H. Weimer and G. Mahler, Phys. Rev. A, 76, 053819 (2007); arXiv:0711.4705v1 [quant-ph] (2007).

    Article  ADS  Google Scholar 

  7. S. De Liberato, D. Gerace, I. Carusotto, and C. Ciuti, Phys. Rev. A, 80, 053810 (2009); arXiv:0906.2706v1 [quant-ph] (2009).

    Article  ADS  Google Scholar 

  8. G. Rempe, H. Walther, and N. Klein, Phys. Rev. Lett., 58, 353–356 (1987).

    Article  ADS  Google Scholar 

  9. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, Phys. Rev. Lett., 76, 1800–1803 (1996).

    Article  ADS  Google Scholar 

  10. S. Bose, I. Fuentes-Guridi, P. L. Knight, and V. Vedral, Phys. Rev. Lett., 87, 050401 (2001); arXiv:quant-ph/0103063v2 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  11. S. Scheel, J. Eisert, P. L. Knight, and M. B. Plenio, J. Modern Opt., 50, 881–889 (2003); arXiv:quant-ph/0207120v1 (2002).

    MathSciNet  ADS  MATH  Google Scholar 

  12. H. Azuma, J. Phys. D, 41, 025102 (2008); arXiv:quant-ph/0604086v6 (2006).

    Article  ADS  Google Scholar 

  13. 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).

    Google Scholar 

  14. N. N. Bogoliubov and N. N. Bogolyubov Jr., Aspects of Polaron Theory [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

  15. N. N. Bogolyubov Jr., V. N. Plechko, and A. S. Shumovsky, Phys. Part. Nucl., 14, 1483–1499 (1983).

    Google Scholar 

  16. N. N. Bogolyubov, F. L. Kien, and A. S. Shumovskii, Theor. Math. Phys., 62, 308–316 (1985).

    Article  Google Scholar 

  17. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, Wiley, New York (1975).

    Google Scholar 

  18. A. O. Caldeira and A. J. Leggett, Annals Phys., 149, 374–456 (1983).

    Article  ADS  Google Scholar 

  19. U. Weiss, Quantum Dissipative Systems (Ser. Mod. Cond. Mat. Phys., Vol. 10), World Scientific, Singapore (1999).

    Book  MATH  Google Scholar 

  20. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford Univ. Press, Oxford (2002).

    MATH  Google Scholar 

  21. A. E. Allahverdyan, R. Serral Gracià, and M. T. Nieuwenhuizen, Phys. Rev. E, 71, 046106 (2005); arXiv:quantph/0411018v1 (2004).

    Article  ADS  Google Scholar 

  22. R. Zwanzig, Phys., 30, 1109–1123 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  23. S. Nakajima, Progr. Theoret. Phys., 20, 948–959 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. R. Zwanzig, J. Chem. Phys., 33, 1338–1341 (1960).

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. N. Bogolyubov Jr..

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 171, No. 1, pp. 116–123, April, 2012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-012-0050-5

Keywords

Navigation