Skip to main content
SpringerLink
Log in

Effect of squeezing and Planck constant dependence in short time semiclassical entanglement

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

Abstract

In this paper, we investigate into the short time semiclassical entanglement of a general class of two-coupled harmonic oscillator system that includes additional nonlinear terms in the potential of the form λ x m y n, such that the sum of the degree m and n equals to a fixed constant. An analytical expression of the short time linear entropy is derived and it shows a clear relationship between the single mode squeezing and the entanglement dynamics. In addition to that, our theoretical analysis has shown that the short time semiclassical entanglement entropy displays a dependence on the Planck constant ħ of the form ħm + n − 2 for this class of systems. By applying our results to the linearly coupled harmonic oscillator, the Barbanis-Contopoulos, the Hénon-Heiles and the Pullen-Edmonds Hamiltonian, we have found a good correspondence between the numerical and analytical results in the short-time regime. Interestingly, our results have demonstrated both analytically and numerically that an appropriate manipulation of initial squeezing can have the significant effect of enhancing the short time semiclassical entanglement between the two subsystems.

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. R.M. Angelo, K. Furuya, Phys. Rev. A 71, 042321 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  2. M. Žnidarič, T. Prosen, Phys. Rev. A 71, 032103 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  3. P. Jacquod, Phys. Rev. Lett. 92, 150403 (2004)

    Article  ADS  Google Scholar 

  4. J.N. Bandyopadhyay, A. Lakshminarayan, Phys. Rev. Lett. 89, 060402 (2002)

    Article  ADS  Google Scholar 

  5. J.N. Bandyopadhyay, A. Lakshminarayan, Phys. Rev. E 69, 016201 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  6. P.A. Miller, S. Sarkar, Phys. Rev. E 60, 1542 (1999)

    Article  ADS  Google Scholar 

  7. H. Fujisaki, T. Miyadera, A. Tanaka, Phys. Rev. E 67, 066201 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  8. S. Chaudhury, A. Smith, B.E. Anderson, S. Ghose, P.S. Jessen, Nature 461, 768 (2009)

    Article  ADS  Google Scholar 

  9. M. Lombardi, A. Matzkin, Phys. Rev. E 83, 016207 (2011)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  11. S.L. Braunstein, P. van Loock, Rev. Mod. Phys. 77, 513 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  12. C. Weedbrook, S. Pirandola, R. Garcia-Patron, N.J. Cerf, T.C. Ralph, J.H. Shapiro, S. Lloyd, Rev. Mod. Phys. 84, 621 (2012)

    Article  ADS  Google Scholar 

  13. F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, R. Werner, Phys. Rev. Lett. 109, 100502 (2012)

    Article  ADS  Google Scholar 

  14. S. Furuichi, A.A. Mahmoud, J. Phys. A 34, 6851 (2001)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. C.H. Er, N.N. Chung, L.Y. Chew, Phys. Scr. 87, 025001 (2013)

    Article  ADS  Google Scholar 

  16. B. Shao, S. Xiang, K. Song, Chin. Phys. B 18, 418 (2009)

    Article  ADS  Google Scholar 

  17. F. Galve, L.A. Pachón, D. Zueco, Phys. Rev. Lett. 105, 180501 (2010)

    Article  ADS  Google Scholar 

  18. X. Wang, B.C. Sanders, Phys. Rev. A 68, 012101 (2003)

    Article  ADS  Google Scholar 

  19. F.A. Beduini, M.W. Mitchell, Phys. Rev. Lett. 111, 143601 (2013)

    Article  ADS  Google Scholar 

  20. G. Contopoulos, Z. Astrophys. 49, 273 (1960)

    ADS  MATH  MathSciNet  Google Scholar 

  21. B. Barbanis, ApJ 71, 415 (1966)

    ADS  Google Scholar 

  22. M. Hénon, C. Heiles, Astron. J. 69, 73 (1964)

    Article  ADS  Google Scholar 

  23. J. Aguirre, J.C. Vallejo, M.A.F. Sanjuán, Phys. Rev. E 64, 066208 (2001)

    Article  ADS  Google Scholar 

  24. R. Barrio, Int. J. Bifurcat. Chaos 16, 2777 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. R. Barrio, W. Borczyk, S. Breiter, Chaos Solitons Fractals 40, 1697 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. F. Blesa, J.M. Seoane, R. Barrio, M.A.F. Sanjuán, Int. J. Bifurcat. Chaos 22, 1230010 (2012)

    Article  Google Scholar 

  27. H.J. Zhao, M.L. Du, Phys. Rev. E 76, 027201 (2007)

    Article  ADS  Google Scholar 

  28. N. Pomphrey, J. Phys. B 7, 1909 (1974)

    Article  ADS  Google Scholar 

  29. R.A. Pullen, A.R. Edmonds, J. Phys. A 14, L477 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  30. N.N. Chung, L.Y. Chew, Phys. Rev. A 76, 032113 (2007)

    Article  ADS  Google Scholar 

  31. N.N. Chung, L.Y. Chew, Phys. Rev. A 80, 012103 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  32. M. Carioli, E.J. Heller, K.B. Møller, J. Chem. Phys. 106, 8564 (1997)

    Article  ADS  Google Scholar 

  33. M. Feit, J.A. Fleck, A. Steiger, J. Comput. Phys. 47, 412 (1982)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  34. M.D. Feit, J.A. Fleck, J. Chem. Phys. 80, 2578 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  35. A. Bogdanov, Y. Bogdanov, K. Valiev, Russian Microelectronics 35, 7 (2006)

    Article  Google Scholar 

  36. S. Parker, S. Bose, M.B. Plenio, Phys. Rev. A 61, 032305 (2000)

    Article  ADS  Google Scholar 

  37. J. Rai, C.L. Mehta, Phys. Rev. A 37, 4497 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  38. F. Hong-Yi, J. VanderLinde, Phys. Rev. A 39, 1552 (1989)

    Article  ADS  Google Scholar 

  39. K.B. Møller, T.G. Jørgensen, J.P. Dahl, Phys. Rev. A 54, 5378 (1996)

    Article  ADS  Google Scholar 

  40. J.N. Hollenhorst, Phys. Rev. D 19, 1669 (1979)

    Article  ADS  Google Scholar 

  41. C.M. Caves, Phys. Rev. D 23, 1693 (1981)

    Article  ADS  Google Scholar 

  42. F. Casas, A. Murua, M. Nadinic, Comput. Phys. Commun. 183, 2386 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  43. V. Fessatidis, J. Mancini, S. Bowen, M. Campuzano, J. Math. Chem. 44, 20 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  44. S.-H. Zhang, Q.-L. Jie, Phys. Rev. A 77, 012312 (2008)

    Article  ADS  Google Scholar 

  45. J.I. Kim, M.C. Nemes, A.F.R. de Toledo Piza, H.E. Borges, Phys. Rev. Lett. 77, 207 (1996)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

    Sijo K. Joseph & Miguel A.F. Sanjuan

  2. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore, Republic of Singapore

    Lock Yue Chew

Authors
  1. Sijo K. Joseph
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lock Yue Chew
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miguel A.F. Sanjuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel A.F. Sanjuan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Joseph, S., Chew, L. & Sanjuan, M. Effect of squeezing and Planck constant dependence in short time semiclassical entanglement. Eur. Phys. J. D 68, 238 (2014). https://doi.org/10.1140/epjd/e2014-50294-0

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2014-50294-0

Keywords

Search

Navigation