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Nonlinear Coherent States and Some of Their Properties

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Abstract

We construct nonlinear coherent states by the application of a deformed displacement operator acting upon the vacuum state and as approximate eigenstates of a deformed annihilation operator. These states are used to evaluate the temporal evolution of the average value of the momentum and the diplacement coordinate as well as their dispersions. We also construct even and odd combinations of these nonlinear coherent states and compute their second order correlation function in order to analyze their statistical behavior.

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References

  1. Glauber, R.J.: Phys. Rev. 130, 2529 (1963)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  3. Glauber, R.J.: Phys. Rev. Lett. 10, 84 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  4. Nieto, M.M., Simmons, L.M.: Phys. Rev. Lett. 41, 207 (1978)

    Article  ADS  Google Scholar 

  5. Nieto, M.M., Simmons, L.M.: Phys. Rev. D 20, 1321 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  6. Nieto, M.M., Simmons, L.M.: Phys. Rev. D 20, 1342 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  7. Gazeau, J.P., Klauder, J.: J. Phys. A: Math. Gen. 32, 123 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Man’ko, V.I., Marmo, G., Zaccaria, F., Sudarshan, E.C.G.: In: Atakishiyev, N., Seligman, T.H. (eds.) Proceedings of the IV Wigner Symposium, p. 421. World Scientific, New York (1996)

    Google Scholar 

  9. de Matos Filho, R.L., Vogel, W.: Phys. Rev. A 54, 4560 (1996)

    Article  ADS  Google Scholar 

  10. Roy, B., Roy, P.: Phys. Lett. A 263, 48 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Roy, B.: Phys. Lett. A 249, 25 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Récamier, J., Jáuregui, R.: J. Opt. B: Quantum Semiclass. Opt. 5, S365 (2003)

    Article  Google Scholar 

  13. Aniello, P., Man’ko, V.I., Marmo, G., Solimeno, S., Zaccaria, F.: J. Opt. B: Quantum Semiclass. Opt. 2, 718 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  14. Man’ko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: Phys. Scripta 55, 528 (1997)

    Article  ADS  Google Scholar 

  15. Landau, L.D., Lifshitz, E.M.: Nonrelativistic Quantum Mechanics, 3th edn. Pergamon, Oxford (1977)

    Google Scholar 

  16. Zhang, W.-M., Feng, D.H., Gilmore, R.: Rev. Mod. Phys. 62, 867 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  17. Sivakumar, S.: J. Opt. B: Quantum and Semiclass. Opt. 2, R61 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  18. Roy, B., Roy, P.: J. Opt. B: Quantum Semiclass. Opt. 2, 65 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  19. Roy, B., Roy, P.: J. Opt. B: Quantum Semiclass. Opt. 2, 505 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  20. Gaziorowitz, S.: Quantum Physics, Chap. VII. Wiley, New York (1974)

    Google Scholar 

  21. Man’ko, V.I., Marmo, G., Porzio, A., Solimeno, S., Zaccaria, F.: Phys. Rev. A 62, 053407 (2000)

    Article  ADS  Google Scholar 

  22. Récamier, J., Mochán, W.L., Gorayeb, M., Paz, J.L., Jáuregui, R.: Int. J. Mod. Phys. B 20, 1851 (2006)

    Article  ADS  Google Scholar 

  23. Carvajal, M., Lemus, R., Frank, A., Jung, C., Ziemniak, E.: Chem. Phys. 260, 105 (2000)

    Article  Google Scholar 

  24. Noel, M.W., Stroud, C.R.: Phys. Rev. Lett. 77, 1913 (1996)

    Article  ADS  Google Scholar 

  25. Gribbin, J.R.: In Search of Schrödinger’s Cat: Quantum Physics and Reality. Bantam Books, Toronto (1984)

    Google Scholar 

  26. Brune, M., Haroche, S., Raimond, J.M., Davidovich, L., Zagury, N.: Phys. Rev. A 45, 5193 (1992)

    Article  ADS  Google Scholar 

  27. Monroe, C., Meekhof, D.M., King, B.E., Wineland, D.J.: Sci. New Ser. 272, 1131 (1996)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apdo. Postal 48-3, Cuernavaca, Morelos, 62251, Mexico

    J. Récamier, M. Gorayeb & W. L. Mochán

  2. Departamento de Química, Universidad Simón Bolívar, Apartado 89000, Caracas, 1080A, Venezuela

    M. Gorayeb & J. L. Paz

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  1. J. Récamier
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  2. M. Gorayeb
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  3. W. L. Mochán
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  4. J. L. Paz
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Correspondence to J. Récamier.

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Récamier, J., Gorayeb, M., Mochán, W.L. et al. Nonlinear Coherent States and Some of Their Properties. Int J Theor Phys 47, 673–683 (2008). https://doi.org/10.1007/s10773-007-9491-2

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  • DOI: https://doi.org/10.1007/s10773-007-9491-2

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