Skip to main content
SpringerLink
Log in

Construction and Properties of Photon-Added su(1) Algebraic Squeezed States†

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We construct a new class of photon-added squeezed states using a single-mode bosonic realization of the su(1) Lie algebra and explore their squeezing properties as a function of the added-photon number. We observe that their squeezing property increases with increase in the number of added photons. In addition, we discuss some basic properties, such as nonorthogonality and resolution of identity. Such states have vast applications, ranging from quantum optics to quantum information processing.

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

  2. R. J. Glauber, Phys. Rev. Lett., 10, 277 (1963).

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

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

  5. I. Ya. Doskoch and M. A. Man’ko, J. Russ. Laser Res., 40, 293 (2019).

  6. I. Ya. Doskoch and M. A. Man’ko, Quantum Reps., 1, 130 (2019).

  7. R. J. Glauber, Quantum Theory of Optical Coherence: Selected Papers and Lectures, Wiley-VCH (2007).

  8. N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light, Imperial College Press, London (2007).

    Book  Google Scholar 

  9. U. L. Andersen, G. Leuchs, and C. Silberhorn, Laser Photon. Rev., 4, 337 (2010).

  10. M. S. Kim, W. Son, V. Bu\( \tilde{z} \)ek, and P. L. Knight, Phys. Rev. A, 65, 032323 (2002).

  11. T. C. Ralph, A. Gilchrist, G. J. Milburn, et al., Phys. Rev. A, 68, 042319 (2003).

  12. H. Kwon, K. C. Tan, T. Volkoff, and H. Jeong, Phys. Rev. Lett., 122, 040503 (2019).

  13. B. Yadin, F. C. Binder, J. Thompson, et al., Phys. Rev. X, 8, 041038 (2018).

  14. K. C. Tan and H. Jeong, Quantum Reps., 1, 151 (2019).

  15. X. Wang, Phys. Rev. A, 64, 022303 (2001).

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

  17. J. Joo, W. J. Munro, and T. P. Spiller, Phys. Rev. Lett., 107, 083601 (2011).

  18. P. Marek and J. Fiurásek, Phys. Rev. A, 82, 014304 (2010).

  19. G. S. Agarwal and K. Tara, Phys. Rev. A, 43, 492 (1991).

  20. G. S. Agarwal and K. Tara, Phys. Rev. A, 46, 485 (1992).

  21. A. Zavatta, S. Viciani, and M. Bellini, Science, 306, 660 (2004).

  22. V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science, 317, 1890 (2007).

  23. O. Barut and L. Girardello, Commun. Math. Phys., 21, 41 (1971).

  24. A. M. Perelomov, Commun. Math. Phys., 26, 222 (1972).

  25. J. R. Klauder, J. Math. Phys., 4, 1055 (1963).

  26. J. R. Klauder, J. Phys. A: Math. Gen., 29, L293 (1996).

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

  28. S. Iqbal, P. Riviere, and F. Saif, Int. J. Theor. Phys., 49, 2540 (2010).

  29. S. Iqbal and F. Saif, J. Russ. Laser Res., 34, 77 (2013).

  30. S. Iqbal and F. Saif, J. Math. Phys., 52, 082105 (2011).

  31. S. Iqbal and F. Saif, Phys. Lett. A, 376, 1531 (2012).

  32. N. Amir and S. Iqbal, J. Math. Phys., 55, 0114101 (2014).

  33. N. Amir and S. Iqbal, J. Math. Phys., 56, 062108 (2015).

  34. N. Amir and S. Iqbal, Commun. Theor. Phys., 66, 41 (2016).

  35. N. Amir and S. Iqbal, Commun. Theor. Phys., 68, 181 (2017).

  36. S. Sivakumar, J. Phys. A: Math. Gen., 32, 3441 (1999).

  37. M. H. Naderi, M. Soltanolkotabi, and R. Roknizadeh, J. Phys. A: Math. Gen., 37, 3225 (2004).

  38. M. N. Hounkonnou and E. B. N. Nkouankam, J. Phys. A: Math. Theor., 42, 025206 (2009).

  39. M. Daoud, Phys. Lett. A, 305, 135 (2002).

  40. D. Popov, J. Phys. A: Math. Gen., 35, 7205 (2002).

  41. O. Safaeian and M. K. Tavassoly, J. Phys. A: Math. Theor., 44, 225301 (2011).

  42. R. Román-Ancheyta, C. González Gutiérez, and J. Recamier, J. Opt. Soc. Am. B, 31, 38 (2014).

  43. S. Dey and V. Hussin, Phys. Rev. A, 93, 053824 (2016).

  44. K. Sodoga, M. N. Hounkonnou, and I. Aremua, Eur. Phys. J. D, 72, 105 (2018).

  45. K. Berrada, J. Math. Phys., 56, 072104 (2015).

  46. H. Monir, N. Amir, and S. Iqbal, Int. J. Theor. Phys., 58, 1776 (2019).

  47. V. Bu\( \tilde{z} \)ek, J. Mod. Opt., 3, 303 (1990).

  48. K. Wodkiewicz and J. H. Eberly, J. Opt. Soc. Am. B, 2, 458 (1985).

  49. C. C. Gerry, J. Phys. A: Math. Gen., 16, L7 (1983);

  50. Y. Aharanov, E. C. Lerner, H. W. Huang, and J. M. Knight, J. Math. Phys., 14, 746 (1973).

  51. C. C. Gerry, Phys. Rev. A, 31, 2721 (1985).

  52. C. C. Gerry, Phys. Rev. A, 35, 2146 (1987).

  53. C. C. Gerry, J. Opt. Soc. Am. B, 8, 685 (1991).

  54. C. C. Gerry and A. Benmoussa, Phys. Rev. A, 71, 062319 (2005).

  55. V. V. Dodonov, M. A. Marchiolli, Ya. A. Korennoy, et al., Phys. Rev. A, 58, 4087 (1998).

  56. V. V. Dodonov, A. B. Klimov, and V. I. Man’ko, Phys. Lett. A, 149, 225 (1990).

  57. R. Schnabel, Phys. Rep., 684, 1 (2017).

  58. A. Otterpohl, F. Sedlmeir, U. Vogl, et al., Optica, 6, 1375 (2019).

  59. C. Xu, L. Zhang, S. Huang, et al., Photon. Res., 7, A14 (2019).

  60. E. Hach, R. Birrittella, P. Alsing, and C. Gerry, J. Opt. Soc. Am. B, 35, 2433 (2018).

  61. E. E. Hach, P. M. Alsing, and C. C. Gerry, Phys. Rev. A, 93, 042104 (2016).

  62. A. M. Mathai and R. K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer, Berlin (1973), Vol. 348.

Download references

Acknowledgments

The financial support provided within the HEC Project No. 10307/Sindh/NRPU/R&D/HEC/2017 is greatly acknowledged.

Author information

Authors and Affiliations

  1. Department of Physics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan

    Hadiah Bint Monir & Shahid Iqbal

Authors
  1. Hadiah Bint Monir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shahid Iqbal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shahid Iqbal.

Additional information

†We dedicate this paper to the memory of Roy Jay Glauber, the great scientist and Nobel Prize Winner, who passed away a year ago, on December 26, 2018. Ad Memoriam of Roy Glauber and George Sudarshan is published in [5, 6] and is also available on link.springer.com/article/10.1007/s10946-019-09805-4 and www.mdpi.com/2624-960X/1/2/13.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Monir, H.B., Iqbal, S. Construction and Properties of Photon-Added su(1) Algebraic Squeezed States†. J Russ Laser Res 41, 1–10 (2020). https://doi.org/10.1007/s10946-020-09843-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-020-09843-3

Keywords

Search

Navigation