Advertisement

Generalized photon-added associated hypergeometric coherent states: characterization and relevant properties

  • Komi Sodoga
  • Isiaka Aremua
  • Mahouton Norbert Hounkonnou
Regular Article
  • 11 Downloads

Abstract

This paper presents the construction of a new set of generalized photon-added coherent states related to associated hypergeometric functions. These states satisfy all required mathematical and physical properties. The associated Stieltjes power-moment problem is explicitly solved by using Meijer’s G-function and the Mellin inversion theorem. Relevant quantum optical and thermal characteristics are investigated. The formalism is applied to particular cases of the associated Hermite, Laguerre, Jacobi polynomials and hypergeometric functions. Their corresponding states exhibit sub-Poissonian photon number statistics.

Graphical abstract

Keywords

Quantum Optics 

References

  1. 1.
    E. Schrödinger, Naturwissenschaften 14, 664 (1926) ADSCrossRefGoogle Scholar
  2. 2.
    R.J. Glauber, Phys. Rev. 130, 2529 (1963) ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    J.R. Klauder, J. Math. Phys. 4, 1055 (1963) Google Scholar
  5. 5.
    J.R. Klauder, J. Math. Phys. 4, 1058 (1963) Google Scholar
  6. 6.
    E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963) ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    A.O. Barut, L. Girardello, Commun. Math. Phys. 21, 41 (1971) ADSCrossRefGoogle Scholar
  8. 8.
    A.M. Perelomov, Generalized coherent states and their applications (Springer, Berlin, 1986) Google Scholar
  9. 9.
    S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets, and Their Generalizations 2nd edition, Theoretical and Mathematical Physics (Springer, New York, 2014) Google Scholar
  10. 10.
    S.T. Ali, J.-P. Antoine, J.-P. Gazeau, U. A. Mueller, Rev. Math. Phys. 7, 1013 (1995) MathSciNetCrossRefGoogle Scholar
  11. 11.
    J.R. Klauder, B.S. Skagerstam, Coherent states: applications in physics and mathematical physics (World Sientific, Singapore, 1985) Google Scholar
  12. 12.
    J.-P. Gazeau, Coherent states in quantum physics (Wiley-, Weinheim, 2009) Google Scholar
  13. 13.
    F.A. Berezin, The method of Second Quantization (Nauka, Moscow, 1986) Google Scholar
  14. 14.
    I. Aremua, J-P. Gazeau, M.N. Hounkonnou, J. Phys. A: Math. Gen. 45, 335302 (2012) Google Scholar
  15. 15.
    I. Aremua, M. N. Hounkonnou, E. Baloïtcha, Rep. Math. Phys. 45, 247 (2015) ADSCrossRefGoogle Scholar
  16. 16.
    N. Cotfas, J. Phys. A: Math. Gen. 35, 9355 (2002) Google Scholar
  17. 17.
    A.N.F. Aleixo, A.B. Balantekin, J. Phys. A: Math. Gen. 37, 8513 (2004) Google Scholar
  18. 18.
    M.N. Hounkonnou, K. Sodoga, J. Phys. A: Math. Gen 38, 7851 (2005) ADSGoogle Scholar
  19. 19.
    G.S. Agarwal, K. Tara, Phys. Rev A. 43, 492 (1991) CrossRefGoogle Scholar
  20. 20.
    G.S. Agarwal, K. Tara, Phys. Rev A. 46, 485 (1992) CrossRefGoogle Scholar
  21. 21.
    V.V. Dodonov, Ya A. Korennoy, V. I. Man’ko, Y. A. Moukhin, Quantum Semiclass. Opt. 8, 413 (1996) Google Scholar
  22. 22.
    V.V. Dodonov, J. Opt. B: Quantum Semiclass. 4, R1 (2002) ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    V.V. Dodonov, V.I. Man’ko, Theory of Nonclassical States of Light (Taylor and Francis, London, 2003) Google Scholar
  24. 24.
    J.M. Sixdeniers, K.A. Penson, J. Phys. A. Math. Gen. 34, 2859 (2001) ADSCrossRefGoogle Scholar
  25. 25.
    J.R. Klauder, K.A. Penson, J.M. Sixdeniers, Phys. Rev. A 64, 013817 (2001) ADSCrossRefGoogle Scholar
  26. 26.
    D. Popov, J. Phys. A: Math. Gen. 35, 7205 (2002) Google Scholar
  27. 27.
    D. Popov, I. Zaharie, S.H. Dong, Czech. J. Phys. 56, 157 (2006) ADSCrossRefGoogle Scholar
  28. 28.
    D. Popov, Electron. J. Theor. Phys. (EJTP) 3, 123 (2006) Google Scholar
  29. 29.
    M.N. Hounkonnou, E.B. Ngompe Nkouankam, J. Phys A: Math. Theor. 42, 025206 (2009) ADSCrossRefGoogle Scholar
  30. 30.
    T. Appl, D.H. Schiller, J. Phys. A: Math. and Gen. 37, 2731 (2004) Google Scholar
  31. 31.
    B. Mojaveri, A. Dehghani, S. Mahmoodi, Phys. Scr. 89, 085202 (2014) ADSCrossRefGoogle Scholar
  32. 32.
    S. Dey, V. Hussin, Phys. Rev. A. 93, 053824 (2016) ADSCrossRefGoogle Scholar
  33. 33.
    V.I. Man’ko, G. Marmo, E.C.G. Sudarshan, F. Zaccaria, Phys. Scr. 55, 528 (1997) ADSCrossRefGoogle Scholar
  34. 34.
    V.I. Man’ko, G. Marmo, S. Solimeno, F. Zaccaria, Int. J. Mod. Phys. A 8, 3577 (1993) ADSCrossRefGoogle Scholar
  35. 35.
    V.I. Man’ko, G. Marmo, S. Solimeno, F. Zaccaria, Phys. Lett. A 176, 173 (1993) ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    K. Sodoga, M.N. Hounkonnou, I. Aremua, Eur. Phys. J. D 72, 105 (2018) ADSCrossRefGoogle Scholar
  37. 37.
    A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (Berlin, Springer, 1991) Google Scholar
  38. 38.
    M. Daoud, Phys. Lett. A. 305, 135 (2002) ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    K. Berrada, J. Math. Phys 56, 072104 (2015) Google Scholar
  40. 40.
    O.I. Marichev, Handbook of integral transforms of higher transcendental functions: theory and algorithmic tables (Ellis Harwood, Chichester, UK, 1983) Google Scholar
  41. 41.
    A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, Integrals and series (Gordon and Breach, New York, 1998) Google Scholar
  42. 42.
    L. Mandel, E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, 1995) Google Scholar
  43. 43.
    K.A. Penson, A.I. Solomon, J. Math. Phys. 40, 2354 (1999) Google Scholar
  44. 44.
    A.M. Mathai, R.K. Saxena, Generalized hypergeometric functions with applications in statistics and physical sciences, Lecture Notes in Mathematics (Springer, Berlin, 1973), vol 348 Google Scholar
  45. 45.
    Y.L. Luke, The special functions and their approximations, (Academic Press, California, 1969), vol 1 Google Scholar
  46. 46.
    S-H. Dong, Factorization Method in Quantum Mechanics, (Springer, Dordrecht, 2007), Google Scholar
  47. 47.
    C.M. Joshi, J.B. McDonald, J. Math. Anal. Appl. 40, 278 (1972) CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Komi Sodoga
    • 1
    • 2
  • Isiaka Aremua
    • 1
    • 2
  • Mahouton Norbert Hounkonnou
    • 2
  1. 1.Université de Lomé, Faculté des Sciences, Département de Physique, Laboratoire de Physique des Matériaux et des Composants à Semi-ConducteursLomé 01Togo
  2. 2.International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-CalaviCotonouRepublic of Benin

Personalised recommendations