International Journal of Theoretical Physics

, Volume 57, Issue 5, pp 1319–1337 | Cite as

Tripartite Entanglement in an Atom-Cavity-Optomechanical System

  • Qinghong Liao
  • Yang Ye
  • Peng Jin
  • Nanrun Zhou
  • Wenjie Nie


We investigate tripartite entanglement in an atom-cavity-optomechanical system consisting of a two-level atom coupled to a cavity with an oscillating mirror at one end. The maximally entangled state between the atom, the field and the oscillating mirror can be prepared in the ideal case. It is shown that the atomic coherent angle that is relatively small makes tripartite entanglement much stronger against dissipative effects in a finite time interval. The parameter k plays a very important role in the oscillating frequency of the tripartite entanglement. More importantly, the π-tangle decays more quickly with the increasing of spontaneous emission rate γ and mean photon number n.


Tripartite entanglement π-tangle Cavity-optomechanical system Quantum information 



This project was supported by National Natural Science Foundation of China (Grant Nos. 61368002 and 61561033), the Foundation for Distinguished Young Scientists of Jiangxi Province (Grant No. 20162BCB23009), the Natural Science Foundation of Jiangxi Province (Grant No. 20161BAB202046), the Open Project Program of CAS Key Laboratory of Quantum Information (Grant No. KQI201704), and Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (Grant No. KF201711).


  1. 1.
    Caves, C.M.: Quantum-mechanical radiation-pressure fluctuations in an interferometer. Phys. Rev. Lett. 45, 75 (1980)ADSCrossRefGoogle Scholar
  2. 2.
    Mancini, S., Giovannetti, V., Vitali, D.: Entangling macroscopic oscillators exploiting radiation pressure. Phys. Rev. Lett. 88, 120401 (2002)ADSCrossRefGoogle Scholar
  3. 3.
    Vitali, D., Gigan, S., Ferreira, A.: Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett. 98, 030405 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    Marquardt, F., Girvin, S.M.: Trend: Optomechanics. Physics 2, 40 (2009)CrossRefGoogle Scholar
  5. 5.
    Aspelmeyer, M., Meystre, P., Schwab, K.C.: Quantum optomechanics. Phys. Today 65, 29 (2012)CrossRefGoogle Scholar
  6. 6.
    Kippenberg, T.J., Vahala, K.J.: Cavity opto-mechanics. Opt. Express 15, 17172 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    Kippenberg, T.J., Vahala, K.J.: Cavity optomechanics: back-action at the mesoscale. Science 321, 1172 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    Abramovici, A., Althouse, W.E., Drever, R.W., Gürsel, Y., Kawamura, S., Raab, F.J., Shoemaker, D., Sievers, L., Spero, R.E., Thorne, K.S., Vogt, R.E., Weiss, R., Whitcomb, S.E., Zucker, M.E.: LIGO: The laser interferometer gravitational-wave observatory. Science 256, 325 (1992)ADSCrossRefGoogle Scholar
  9. 9.
    Vitali, D., Mancini, S., Tombesi, P.: Optomechanical scheme for the detection of weak impulsive forces. Phys. Rev. A 64, 188 (2001)CrossRefGoogle Scholar
  10. 10.
    Geraci, A.A., Papp, S.B., Kitching, J.: Short-range force detection using optically cooled levitated microspheres. Phys. Rev. Lett. 105, 101101 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    Lamoreaux, S.K.: Casimir forces: Still surprising after 60 years. Phys. Today 60, 40 (2007)CrossRefGoogle Scholar
  12. 12.
    Stannigel, K., Rabl, P., Sørensen, A. S.: Optomechanical transducers for long-distance quantum communication. Phys. Rev. Lett. 105, 6322 (2010)CrossRefGoogle Scholar
  13. 13.
    Genes, C., Vitali, D., Tombesi, P.: Emergence of atom-light-mirror entanglement inside an optical cavity. Phys. Rev. A 77, 18 (2008)Google Scholar
  14. 14.
    Meiser, D., Meystre, P.: Coupled dynamics of atoms and radiation pressure driven interferometers. Phys. Rev. A: At. Mol. Opt. Phys. 73, 501 (2006)CrossRefGoogle Scholar
  15. 15.
    Ian, H., Gong, Z.R., Liu, Y.X.: Cavity optomechanical coupling assisted by an atomic gas. Phys. Rev. A 78, 124 (2008)CrossRefGoogle Scholar
  16. 16.
    Marshall, W., Simon, C., Penrose, R.: Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Bose, S., Jacobs, K., Knight, P.L.: A quantum optical scheme to probe the decoherence of a macroscopic object. Phys. Rev. A 59, 3204 (1999)ADSCrossRefGoogle Scholar
  18. 18.
    Mancini, S., Tombesi, P.: Quantum noise reduction by radiation pressure. Phys. Rev. A: At. Mol. Opt. Phys. 49, 4055 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    Wang, Y.M., Liu, B., Lian, J.L.: A scheme for detecting the atom-field coupling constant in the Dicke superradiation regime using hybrid cavity optomechanical system. Opt. Express 20, 10106 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Zhou, L., Han, Y., Jing, J.T.: Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence. Phys. Rev. A 83, 052117 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    Hammerer, K., Aspelmeyer, M., Polzik, E.S.: Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles. Phys. Rev. Lett. 102, 020501 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Liu, N., Li, J.Q., Liang, J.Q.: Entanglement in a tripartite cavity-optomechanical system. Int. J. Theor. Phys. 52, 706 (2013)CrossRefzbMATHGoogle Scholar
  23. 23.
    James, D.F.V., Jerke, J.: Effective Hamiltonian theory and its applications in quantum information. Can. J. Phys. 85, 625 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    Ou, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A 75, 062308 (2007)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Qinghong Liao
    • 1
    • 2
  • Yang Ye
    • 1
  • Peng Jin
    • 1
  • Nanrun Zhou
    • 1
  • Wenjie Nie
    • 3
  1. 1.Department of Electronic Information EngineeringNanchang UniversityNanchangChina
  2. 2.CAS Key Laboratory of Quantum InformationUniversity of Science and Technology of ChinaHefeiChina
  3. 3.Department of Applied PhysicsEast China Jiaotong UniversityNanchangChina

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