Skip to main content
SpringerLink
Log in

Matrix diagonalization and exact solution of the k-photon Jaynes–Cummings model

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We study and exactly solve the two-photon and k-photon Jaynes–Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the SU(2) group and let us diagonalize the Hamiltonian of these models by properly choosing the coherent state parameters of the transformation. Finally, we explicitly obtain the energy spectrum and eigenfunctions for each model.

Graphical abstract

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

    Article  Google Scholar 

  2. V.V. Dodonov, V.I. Man’ko (Eds.), Theory of Nonclassical States of Light (Taylor and Francis, London, 2003)

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

    Article  ADS  Google Scholar 

  4. S. Haroche, J.M. Raimond, Exploring the Quantum: Atoms, Cavities and Photons (Oxford University Press, Oxford, 2007)

  5. J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  6. J.R. Kuklinski, J. Madajczyk, Phys. Rev. A 37, 3175 (1988)

    Article  ADS  Google Scholar 

  7. P. Goy, J.M. Raimond, M. Gross, S. Haroche, Phys. Rev. Lett. 50, 1903 (1983)

    Google Scholar 

  8. M. Brune et al., Phys. Rev. Lett. 76, 1800 (1996)

    Article  ADS  Google Scholar 

  9. C. Guerlin et al., Nature 448, 889 (2007)

    Article  ADS  Google Scholar 

  10. Y. Nogami, F.M. Toyama, Can. J. Phys. 74, 114 (1996)

    Article  ADS  Google Scholar 

  11. F.M. Toyama, Y. Nogami, F.A.B. Coutinho, J. Phys. A: Math. Gen. 30, 2585 (1997)

    Article  ADS  Google Scholar 

  12. R. Szmytkowski, M. Gruchowski, J. Phys. A: Math. Gen. 34, 4991 (2001)

    Article  ADS  Google Scholar 

  13. D. Ojeda-Guillén, R.D. Mota, V.D. Granados, J. Math. Phys. 57, 062104 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  14. A. Bermudez, M.A. Martin-Delgado, E. Solano, Phys. Rev. A 76, 041801 (2007)

    Article  ADS  Google Scholar 

  15. A. Bermudez, M. A. Martin-Delgado, A. Luis, Phys. Rev. A 77, 063815 (2008)

    Article  ADS  Google Scholar 

  16. E.A. Kochetov, J. Phys. A 20, 2433 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  17. V. Buzek, Czech. J. Phys. B 39, 757 (1989)

    Article  ADS  Google Scholar 

  18. S.C. Gou, Phys. Rev. A 48, 3233 (1993)

    Article  ADS  Google Scholar 

  19. E. Choreño, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Ann. Phys. 387, 121 (2017)

    Article  ADS  Google Scholar 

  20. L. Lamata et al., New J. Phys. 13, 095003 (2011)

    Article  ADS  Google Scholar 

  21. A. Retzker, E. Solano, B. Reznik, Phys. Rev. A 75, 022312 (2007)

    Article  ADS  Google Scholar 

  22. W. Kopylov et al., Phys. Rev. A 92, 063832 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. C. Sun, N. Sinitsyn, Phys. Rev. A 94, 033808 (2016)

    Article  ADS  Google Scholar 

  24. M. Chaichian, D. Ellinas, P. Kulish, Phys. Rev. Lett. 65, 980 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  25. B. Buck, C.V. Sukumar, Phys. Lett. A 81, 132 (1981)

    Article  ADS  Google Scholar 

  26. C.C. Gerry, Phys. Rev. A 37, 2683 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  27. A. Joshi, R.R. Puri, Phys. Rev. A 45, 5056 (1992)

    Article  ADS  Google Scholar 

  28. V. Bartzis, N. Nayak, J. Opt. Soc. Am. B 8, 1779 (1991)

    Article  ADS  Google Scholar 

  29. P. Zhou, J.S. Peng, Phys. Rev. A 44, 3331 (1991)

    Article  ADS  Google Scholar 

  30. T. Nasreen, M.S.K. Razmi, J. Opt. Soc. Am. B 10, 1292 (1993)

    Article  ADS  Google Scholar 

  31. K.M. Ng, C.F. Lo, K.L. Liu, Eur. Phys. J. D 6, 119 (1999)

    Article  ADS  Google Scholar 

  32. C.V. Sukumar, B. Buck, Phys. Lett. A 83, 211 (1981)

    Article  ADS  Google Scholar 

  33. A.S. Shumovsky, F.L. Kien, E.I. Aliskenderov, Phys. Lett. A 124, 351 (1987)

    Article  ADS  Google Scholar 

  34. W. Vogel, D.G. Welsch, Phys. Rev. A 40, 7113 (1989)

    Article  ADS  Google Scholar 

  35. H.R. Baghshahi, M.K. Tavassoly, A. Behjat, Chin. Phys. B 23, 074203 (2014)

    Article  Google Scholar 

  36. R. Koc, H. Tutunculer, M. Koca, E. Olgar, Ann. Phys. 319, 333 (2005)

    Article  ADS  Google Scholar 

  37. H. Panahi, S.A. Rad, Int. J. Theor. Phys. 52, 4068 (2013)

    Article  Google Scholar 

  38. C.C. Gerry, Phys. Rev. A 39, 3204 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  39. D. Ojeda-Guillén, R.D. Mota, V.D. Granados, J. Math. Phys. 55, 042109 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  40. D. Ojeda-Guillén, R.D. Mota, V.D. Granados, Commun. Theor. Phys. 64, 34 (2015)

    Article  ADS  Google Scholar 

  41. A. Vourdas, Phys. Rev. A 41, 1653 (1990)

    Article  ADS  Google Scholar 

  42. A.M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986)

  43. F.T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, Phys. Rev. A 6, 2211 (1972)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Delegación Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico

    Enrique Choreño & Víctor David Granados

  2. Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico

    Didier Ojeda-Guillén

Authors
  1. Enrique Choreño
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Didier Ojeda-Guillén
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Víctor David Granados
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Enrique Choreño.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Choreño, E., Ojeda-Guillén, D. & Granados, V.D. Matrix diagonalization and exact solution of the k-photon Jaynes–Cummings model. Eur. Phys. J. D 72, 142 (2018). https://doi.org/10.1140/epjd/e2018-90106-y

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2018-90106-y

Keywords

Search

Navigation