Skip to main content
SpringerLink
Log in

A class of nonlinear coherent states attached to Tsallis q-exponential

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

Abstract.

We construct a new class of nonlinear coherent states (NCS's) based on Tsallis q -exponential with \(1 < q\leq 2\). The special cases q = 2 and \( q\rightarrow 1\) recover the well-known harmonious states and canonical coherent states, respectively. Some non-classical properties are then studied. It has been found that this class of NCS's exhibits quadrature squeezing in the p component, amplitude squared squeezing in the Y component and negativity of Wigner function, however, it obeys a super-Poissonian statistics and exhibits a bunching behavior. In addition, we introduce nonlinear two-mode squeezed vacuum states (NTSVSs) attached to Tsallis q-exponential. These states are reduced to the well-known two-mode squeezed vacuum states (TSVSs) and pair coherent states (PCSs) when \( q\rightarrow 1\) and q = 2, respectively. Furthermore, the entanglement of the NTSVSs is examined by evaluating the linear entropy. Finally, we investigate the quantum teleportation of a coherent state using a NTSVS as a shared entangled resource instead of a TSVS. It is shown that the fidelity of teleportation depends on the nonlinearity function f(n) and recovers its standard expression in the linear limit \(f(n)=1\).

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. S. Bo-sture, Coherent States: Applications in Physics and Mathematical Physics (World Scientific, 1985)

  2. S.J. van Enk, O. Hirota, Phys. Rev. A 64, 022313 (2001)

    Article  ADS  Google Scholar 

  3. F. Grosshans, P. Grangier, Phys. Rev. Lett. 88, 057902 (2002)

    Article  ADS  Google Scholar 

  4. T.C. Ralph, A. Gilchrist, G.J. Milburn, W.J. Munro, S. Glancy, Phys. Rev. A 68, 042319 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  6. E. Schrödinger, Naturwissenschaften 14, 664 (1926)

    Article  ADS  Google Scholar 

  7. J.P. Gazeau, Coherent States in Quantum Physics (Wiley, 2009)

  8. M.D. Darareh, M. Naderi, M. Soltanolkotabi, Opt. Commun. 282, 4577 (2009)

    Article  ADS  Google Scholar 

  9. K.P. Seshadreesan, J.P. Dowling, G.S. Agarwal, Phys. Scr. 90, 074029 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. V. Man'ko, G. Marmo, E. Sudarshan, F. Zaccaria, Phys. Scr. 55, 528 (1997)

    Article  ADS  Google Scholar 

  12. L. Biedenharn, J. Phys. A 22, L873 (1989)

    Article  ADS  Google Scholar 

  13. A. Macfarlane, J. Phys. A 22, 4581 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  14. B. Roy, P. Roy, J. Opt. B 2, 65 (2000)

    Article  ADS  Google Scholar 

  15. S. Mancini, V.I. Man'ko, J. Opt. B 4, S117 (2002)

    Article  ADS  Google Scholar 

  16. E. Sudarshan, Int. J. Theor. Phys. 32, 1069 (1993)

    Article  Google Scholar 

  17. K. Penson, A. Solomon, J. Math. Phys. 40, 2354 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  18. M. Tavassoly, Opt. Commun. 283, 5081 (2010)

    Article  ADS  Google Scholar 

  19. R. Roknizadeh, M. Tavassoly, J. Phys. A 37, 8111 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  20. R. Roknizadeh, M. Tavassoly, J. Math. Phys. 46, 042110 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  21. G. Agarwal, K. Tara, Phys. Rev. A 43, 492 (1991)

    Article  ADS  Google Scholar 

  22. A. Zavatta, S. Viciani, M. Bellini, Phys. Rev. A 72, 023820 (2005)

    Article  ADS  Google Scholar 

  23. S. Sivakumar, J. Phys. A 32, 3441 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  24. A. Barut, L. Girardello, Commun. Math. Phys. 21, 41 (1971)

    Article  ADS  Google Scholar 

  25. V. Dodonov, J. Opt. B 4, R1 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  26. M.B. Harouni, R. Roknizadeh, M.H. Naderi, J. Phys. B 41, 225501 (2008)

    Article  ADS  Google Scholar 

  27. A. Mahdifar, W. Vogel, T. Richter, R. Roknizadeh, M.H. Naderi, Phys. Rev. A 78, 063814 (2008)

    Article  ADS  Google Scholar 

  28. M.R. Setare, P. Majari, Eur. Phys. J. Plus 132, 458 (2017)

    Article  Google Scholar 

  29. M. Setare, P. Majari, Phys. Lett. A 382, 428 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. F. Ewert, P. van Loock, arXiv:1708.08834 (2017)

  31. C. Tsallis, J. Stat. phys. 52, 479 (1988)

    Article  ADS  Google Scholar 

  32. C. Tsallis, Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World (Springer Science & Business Media, 2009)

  33. R.G. DeVoe, Phys. Rev. Lett. 102, 063001 (2009)

    Article  ADS  Google Scholar 

  34. E. Lutz, F. Renzoni, Nat. Phys. 9, 615 (2013)

    Article  Google Scholar 

  35. R. Boudjema, A.H. Hamici, M. Hachemane, A. Smida, Quantum Inf. Process. 15, 551 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  36. T. qiang Song, H. yi Fan, J. Phys. A 35, 1071 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  37. F. Hong-Yi, J. Vanderlinde, Phys. Rev. A 39, 2987 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  38. L. Vaidman, Phys. Rev. A 49, 1473 (1994)

    Article  ADS  Google Scholar 

  39. S.L. Braunstein, H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)

    Article  ADS  Google Scholar 

  40. J. Messamah, F.E. Schroeck, M. Hachemane, A. Smida, A.H. Hamici, Quantum Inf. Process. 14, 1035 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  41. F.E. Schroeck Jr, Quantum Mechanics on Phase Space, Vol. 74 (Springer Science & Business Media, 2013)

  42. E.P. Borges, J. Phys. A 31, 5281 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  43. J. Recamier, M. Gorayeb, W. Mochán, J. Paz, Int. J. Quantum Chem. 106, 3160 (2006)

    Article  ADS  Google Scholar 

  44. J.R. Klauder, J. Math. Phys. 4, 1058 (1963)

    Article  ADS  Google Scholar 

  45. J. Klauder, K. Penson, J.M. Sixdeniers, Phys. Rev. A 64, 013817 (2001)

    Article  ADS  Google Scholar 

  46. F. Oberhettinger, Tables of Mellin Transforms (Springer Science & Business Media, 2012)

  47. L. Mandel, Opt. Lett. 4, 205 (1979)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  50. N. Lütkenhaus, S.M. Barnett, Phys. Rev. A 51, 3340 (1995)

    Article  ADS  Google Scholar 

  51. A. Kenfack, K. Zyczkowski, J. Opt. B 6, 396 (2004)

    Article  ADS  Google Scholar 

  52. C. Cohen-Tannoudji, B. Diu, F. Laloë, Mécanique Quantique, tome 1 (Hermann, 1973)

  53. G.S. Agarwal, Phys. Rev. Lett. 57, 827 (1986)

    Article  ADS  Google Scholar 

  54. C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  55. G.S. Agarwal, A. Biswas, J. Opt. B 7, 350 (2005)

    Article  ADS  Google Scholar 

  56. E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime: A Consistent Unification of Relativity and Quantum Theory based on Stochastic Spaces, Vol. 4 (D. Reidel Publishing Company, Dordercht, 1984)

  57. F.E. Schroeck Jr., J. Phys. A 45, 065303 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  58. E. Arthurs, J.L. Kelly, Bell Syst. Techn. J. 44, 725 (1965)

    Article  Google Scholar 

  59. P. Busch, Int. J. Theor. Phys. 24, 63 (1985)

    Article  MathSciNet  Google Scholar 

  60. P. Busch, M. Grabowski, P.J. Lahti, Operational Quantum Physics, Vol. 31 (Springer Science & Business Media, 1997)

  61. H.F. Hofmann, T. Ide, T. Kobayashi, A. Furusawa, Phys. Rev. A 62, 062304 (2000)

    Article  ADS  Google Scholar 

  62. N.T.X. Hoai, T.M. Duc, Int. J. Mod. Phys. B 30, 1650032 (2016)

    Article  ADS  Google Scholar 

  63. A. Gabris, G.S. Agarwal, Int. J. Quantum Inf. 5, 17 (2007)

    Article  Google Scholar 

  64. J. Katriel, A.I. Solomon, Phys. Rev. A 49, 5149 (1994)

    Article  ADS  Google Scholar 

  65. C. Quesne, J. Phys. A 35, 9213 (2002)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Physique Théorique, Faculté de Physique, Université des Sciences et de la Technologie Houari Boumedienne, BP 32 El-Alia, 16111, Alger, Algeria

    Abdelhak Bendjeffal, Abdallah Smida, Juba Messamah & Mahmoud Hachemane

Authors
  1. Abdelhak Bendjeffal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdallah Smida
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juba Messamah
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mahmoud Hachemane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdelhak Bendjeffal.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bendjeffal, A., Smida, A., Messamah, J. et al. A class of nonlinear coherent states attached to Tsallis q-exponential. Eur. Phys. J. Plus 134, 330 (2019). https://doi.org/10.1140/epjp/i2019-12865-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2019-12865-9

Search

Navigation