Skip to main content
SpringerLink
Log in

Symplectic tomography of the Jaynes-Cummings model

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We derive equations describing quantum evolution for the classical-like tomographic-probability-distribution function for the Jaynes-Commings model. Different representations for the field part of the total density matrix are considered.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Schrödinger,Ann. Phys.,79, 489 (1926).

    MATH  Google Scholar 

  2. J. von Neumann,Göttingenische Nachrichten,11, 245 (November 1927);Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).

    Google Scholar 

  3. E. Wigner,Phys. Rev.,40, 749 (1932).

    Article  MATH  ADS  Google Scholar 

  4. R. J. Glauber,Phys. Rev.,131, 2766 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  5. E. C. G. Sudarshan,Phys. Rev. Lett.,10, 177 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  6. K. Husimi,Proc. Phys. Math. Soc. Jpn,23, 264 (1940).

    Google Scholar 

  7. K. Vogel and H. Risken,Phys. Rev. A,40, 2847 (1989).

    Article  ADS  Google Scholar 

  8. S. Mancini, V. I. Man'ko, and P. Tombesi,Quantum Semiclass. Opt.,7, 615 (1995).

    Article  ADS  Google Scholar 

  9. S. Mancini, V. I. Man'ko, and P. Tombesi,Phys. Lett. A,213, 1 (1996).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. S. Mancini, V. I. Man'ko, and P. Tombesi,Found. Phys.,27, 801 (1997).

    MathSciNet  ADS  Google Scholar 

  11. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani,Phys. Rev. Lett.,70, 1244 (1993).

    Article  ADS  Google Scholar 

  12. S. Wallentowitz and W. Vogel,Phys. Rev. A,53, 4528 (1996).

    Article  ADS  Google Scholar 

  13. K. Banaszek and K. Wodkiewicz,Phys. Rev. Lett.,76, 4344 (1996).

    Article  ADS  Google Scholar 

  14. S. Mancini, P. Tombesi, and V. I. Man'ko,Europhys. Lett.,37, 79 (1996).

    Article  ADS  Google Scholar 

  15. V. V. Dodonov and V. I. Man'ko,Phys. Lett., A,229, 335 (1997).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. O. V. Man'ko and V. I. Man'ko,JETP,85, 430 (1997).

    Article  ADS  Google Scholar 

  17. G. S. Agarwal,Phys. Rev. A,57, 671 (1998).

    Article  ADS  Google Scholar 

  18. V. A. Andreev and V. I. Man'ko,JETP,87, 239 (1998).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  20. H. L. Yoo and J. H. Eberly,Phys. Rep.,118, 239 (1985).

    Article  ADS  Google Scholar 

  21. B. W. Shore and P. L. Knight,J. Mod. Opt.,40, 1195 (1993).

    MATH  MathSciNet  ADS  Google Scholar 

  22. J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon,Phys. Rev. Lett.,58, 353 (1987).

    Article  Google Scholar 

  23. J. R. Kuklinski and J. L. Madajczyk,Phys. Rev. A,37, 3175 (1988).

    Article  ADS  Google Scholar 

  24. K. Vogel, V. M. Akulin and W. P. Schleich,Phys. Rev. Lett.,71, 1816 (1993).

    Article  ADS  Google Scholar 

  25. C. Monroe, D. M. Meekhof, and D. T. Wineland,Science,272, 1131 (1996).

    MathSciNet  ADS  Google Scholar 

  26. L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche,Phys. Rev. A,53, 1295 (1996).

    Article  ADS  Google Scholar 

  27. M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche,Phys. Rev. Lett.,77, 4887 (1996).

    Article  ADS  Google Scholar 

  28. S. Mancini, V. I. Man'ko, and P. Tombesi,J. Mod. Opt.,44, 2281 (1997).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. F. T. Arecchi, E. Courtens, R. Gilmor, and H. Thomas,Phys. Rev. A,6, 2211 (1972).

    Article  ADS  Google Scholar 

  30. E. H. Lieb,Comm. Math. Phys.,31, 327 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. L. Narducchi, C. Bowden, V. Bluemel, G. Garrazana, and R. Tuft,Phys. Rev. A,11, 973 (1975).

    Article  ADS  Google Scholar 

  32. J. M. Radcliffe,J. Phys. A,4, 313 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  33. S. Mancini, V. I. Man'ko, and P. Tombesi,Quantum Semiclass. Opt.,9, 987 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  34. V. I. Man'ko, “Quantum mechanics and classical probability theory,” in: B. Gruber and M. Ramek (eds.),Symmetries in Science IX, Plenum Press, New York (1997), p. 215.

    Google Scholar 

  35. Olga Man'ko and V. I. Man'ko,J. Russ. Laser Res.,18, 407 (1997).

    Google Scholar 

  36. K. E. Cahill and R. J. Glauber,Phys. Rev.,177, 1882 (1969).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, S.R., Guadalajara, Jal., Mexico

    A. B. Klimov

  2. P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Pr. 53, 117924, Moscow, Russia

    V. I. Man'ko

Authors
  1. A. B. Klimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Man'ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klimov, A.B., Man'ko, V.I. Symplectic tomography of the Jaynes-Cummings model. J Russ Laser Res 21, 205–213 (2000). https://doi.org/10.1007/BF02508947

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02508947

Keywords

Search

Navigation