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International Journal of Theoretical Physics

, Volume 57, Issue 9, pp 2802–2813 | Cite as

κ-Deformed Photon and Jaynes-Cummings Model

  • Won Sang Chung
Article
  • 17 Downloads

Abstract

In this paper, we discuss the κ-deformed boson algebra. We present the infinite dimensional representation of this algebra. Assuming that the photon obeys the κ-deformed algebra instead of the ordinary boson algebra, we discuss the κ-deformed quantum optical electromagnetic field whose classical Hamiltonian is written in terms of an infinite set of real harmonic oscillators. We also discuss the second quantization of light when we regard the photon as the quantum particle obeying the κ-deformed boson algebra. Finally we discuss the interaction between a two-level atom coupled to a single κ-photon.

Keywords

κ-deformed boson κ-photon 

Notes

Acknowledgements

I acknowledge to reviewer for helpful comments. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2015R1D1A1A01057792) and by Development Fund Foundation, Gyeongsang National University, 2018.

References

  1. 1.
    Arik, M., Coon, D.: J. Math. Phys. 17, 524 (1976)ADSCrossRefGoogle Scholar
  2. 2.
    Macfarlane, A.J.: J. Phys. A 22, 4581 (1989)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Biedenharn, L.: J. Phys. A 22, L873 (1990)CrossRefGoogle Scholar
  4. 4.
    Daskaloyannis, C.: J. Phys. A: Math. Gen. 24, L789–L794 (1991)ADSCrossRefGoogle Scholar
  5. 5.
    Fu, H.-C., Sasaki, R.: J. Phys. A: Math. Gen. 29, 4049 (1996)ADSCrossRefGoogle Scholar
  6. 6.
    Quesne, C., Vansteenkiste, N.: Phys. Lett. A 240, 21 (1998)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Quesne, C., Vansteenkiste, N.: Int. J. Theor. Phys. 39, 1175 (2000)CrossRefGoogle Scholar
  8. 8.
    Quesne, C.: Phys. Lett. A 272, 313 (2000) + erratum Phys. Lett. A 275, 313 (2000)Google Scholar
  9. 9.
    Quesne, C.: Mod. Phys. Lett. A 18, 515 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    Antoine, J.P., Gazeau, J.P., Monceau, P., Klauder, J.R., Penson, K.A.: J. Math. Phys. 42, 2349 (2001)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Gazeau, J., Champagne, B.: Algebraic methods in physics. CRM Series in Mathematical Physics. pp. 65–79 (2001)Google Scholar
  12. 12.
    Daoud, M., Kibler, M.: J. Math. Phys. 47, 122108 (2006)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Daoud, M., Kibler, M.R.: J. Phys. A: Math. Theor. 43, 115303 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    Daoud, M., Kibler, M.: J. Math. Phys. 52, 081201 (2011)CrossRefGoogle Scholar
  15. 15.
    Daoud, M., Kibler, M.: J. Phys. A 45, 244036 (2012)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Chung, W.S.: Mod. Phys. Lett. A 28, 1350115 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    Shore, B., Knight, P.: J. Mod. Opt. 40, 1195 (1993)ADSCrossRefGoogle Scholar
  18. 18.
    Katriel, J., Solomon, A.: Phys. Rev. A 49, 5149 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    Jaynes, E.T., Cummings, F.W.: Proc. IEE 51, 89 (1963)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics and Research Institute of Natural Science, College of Natural ScienceGyeongsang National UniversityJinjuKorea

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