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Controlling photon–phonon entanglement in a three-mode optomechanical system

  • Regular Article - Quantum Optics
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Abstract

In this paper, we consider a three-mode optomechanical system, where two movable mirrors are coupled to a single cavity mode with different optomechanical coupling strengths. Instead of the phonon–phonon entanglement which has often been studied, here we focus on the photon–phonon entanglement. Using the logarithmic negativity, we found that stationary entanglement strongly depends on the temperature, dissipation rates, and optomechanical couplings. Furthermore, the system at hand exhibits an entanglement transfer that can be controlled using only one of the two optomechanical couplings. However, manipulating optomechanical couplings is limited by the stability conditions.

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Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This work is a theoretical study and we have not used any data.]

References

  1. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  2. B.M. Terhal, Theor. Comput. Sci. 287, 313 (2002)

    Article  Google Scholar 

  3. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  Google Scholar 

  4. O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  5. C.H. Bennett, D.P. DiVincenzo, Nature 404, 247 (2000)

    Article  ADS  Google Scholar 

  6. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  7. A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  8. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  9. C.H. Bennett, S.J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  10. V. Scarani, H. Bechmann-Pasquinucci, N.J. Cerf, M. Dusek, N. Lütkenhaus, M. Peev, Rev. Mod. Phys. 81, 1301 (2009)

    Article  ADS  Google Scholar 

  11. D. Leibfried, E. Knill, S. Seidelin, J. Britton, R.B. Blakestad, J. Chiaverini, D.B. Hume, W.M. Itano, J.D. Jost, C. Langer, R. Ozeri, R. Reichle, D.J. Wineland, Nature 438, 639 (2005)

    Article  ADS  Google Scholar 

  12. H. Häffner, W. Hänsel, C.F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U.D. Rapol, M. Riebe, P.O. Schmidt, C. Becher, O. Gühne, W. Dür, R. Blatt, Nature 438, 643 (2005)

    Article  ADS  Google Scholar 

  13. P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, Science 320, 1326 (2008)

    Article  ADS  Google Scholar 

  14. P. Meystre, Ann. Phys. 525, 215 (2013)

    Article  Google Scholar 

  15. M. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014)

    Article  ADS  Google Scholar 

  16. D. Vitali, S. Gigan, A. Ferreira, H.R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, M. Aspelmeyer, Phys. Rev. Lett. 98, 030405 (2007)

    Article  ADS  Google Scholar 

  17. M. Pinard, A. Dantan, D. Vitali, O. Arcizet, T. Briant, A. Heidmann, Europhys. Lett. 72, 747 (2005)

    Article  ADS  Google Scholar 

  18. D. Vitali, S. Mancini, P. Tombesi, J. Phys. A Math. Theor. 40, 8055 (2007)

    Article  ADS  Google Scholar 

  19. J. Zhang, K. Peng, S.L. Braunstein, Phys. Rev. A 68, 013808 (2003)

    Article  ADS  Google Scholar 

  20. E.A. Sete, H. Eleuch, C.H.R. Ooi, JOSA B 31, 2821 (2014)

    Article  ADS  Google Scholar 

  21. J. Li, G. Li, S. Zippilli, D. Vitali, T. Zhang, Phys. Rev. A 95, 043819 (2017)

    Article  ADS  Google Scholar 

  22. J. Li, I.M. Haghighi, N. Malossi, S. Zippilli, D. Vitali, New J. Phys. 17, 103037 (2015)

    Article  ADS  Google Scholar 

  23. J.H. Liu, Y.B. Zhang, Y.F. Yu, Z.M. Zhang, Opt. Express 25, 7592 (2017)

    Article  ADS  Google Scholar 

  24. J.H. Liu, Y.B. Zhang, Y.F. Yu, Z.M. Zhang, Front. Phys. 14, 12601 (2019)

    Article  ADS  Google Scholar 

  25. G. Li, W. Nie, X. Li, M. Li, A. Chen, Y. Lan, Sci. China Phys. Mech. Astron. 62, 100311 (2019)

    Article  ADS  Google Scholar 

  26. W.P. Bowen, G.J. Milburn, Quantum Optomechanics (Taylor and Francis, Boca Raton, 2015)

    Book  Google Scholar 

  27. C.K. Law, Phys. Rev. A 51, 2537 (1995)

    Article  ADS  Google Scholar 

  28. C. Gardiner, P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, Berlin, 2004)

    MATH  Google Scholar 

  29. V. Giovannetti, D. Vitali, Phys. Rev. A 63, 023812 (2001)

    Article  ADS  Google Scholar 

  30. G.J. Milburn, M.J. Woolley, Acta Physica Slovaca 61, 483 (2011)

    ADS  Google Scholar 

  31. E.X. DeJesus, C. Kaufman, Phys. Rev. A 35, 5288 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  32. A. Mari, J. Eisert, Phys. Rev. Lett. 103, 213603 (2009)

    Article  ADS  Google Scholar 

  33. P.C. Parks, V. Hahn, Stability Theory (Prentice Hall, Upper Saddle River, 1993)

    MATH  Google Scholar 

  34. R. Simon, Phys. Rev. Lett. 84, 2726 (2000)

    Article  ADS  Google Scholar 

  35. G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  36. G. Adesso, A. Serafini, F. Illuminati, Phys. Rev. Lett. 92, 087901 (2004)

    Article  ADS  Google Scholar 

  37. S. Gröblacher, K. Hammerer, M.R. Vanner, M. Aspelmeyer, Nature 460, 724 (2009)

    Article  ADS  Google Scholar 

  38. Z. Ficek, R. Tanaś, Phys. Rev. A 74, 024304 (2006)

    Article  ADS  Google Scholar 

  39. U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, Cambridge, 2005)

    MATH  Google Scholar 

  40. T.A. Palomaki, J.D. Teufel, R.W. Simmonds, K.W. Lehnert, Science 342, 710 (2013)

    Article  ADS  Google Scholar 

  41. Q. Zheng, J. Xu, Y. Yao, Y. Li, Phys. Rev. A 94, 052314 (2016)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. EPTHE, Department of Physics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco

    Abderrahim Lakhfif, Jamal El Qars & Mostafa Nassik

  2. Department of Physics, Faculty of Applied Sciences, Ait-Melloul, Ibn Zohr University, Agadir, Morocco

    Jamal El Qars

Authors
  1. Abderrahim Lakhfif
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  2. Jamal El Qars
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  3. Mostafa Nassik
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Correspondence to Abderrahim Lakhfif.

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Lakhfif, A., El Qars, J. & Nassik, M. Controlling photon–phonon entanglement in a three-mode optomechanical system. Eur. Phys. J. D 75, 189 (2021). https://doi.org/10.1140/epjd/s10053-021-00205-5

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  • DOI: https://doi.org/10.1140/epjd/s10053-021-00205-5

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