Skip to main content
SpringerLink
Log in

Constructing Robust Entangled Coherent GHZ and W States via a Cavity QED System

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Using a system of three distant cavities, we propose a method for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entangled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negligible the destruction of entanglement due to dissipation arises from photon losses, is effectively suppressed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Cirac, J. I., Ekert, A. K., Huelga, S. F., Macchiavello, C.: Phys. Rev. A 59, 4249 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  2. Hartmann, M., Brandao, F.G.S.L., Plenio, M.B.: Nat. Phys. 2, 849 (2006)

    Article  Google Scholar 

  3. Angelakis, D. G., Santos, M. F., Bose, S.: Phys. Rev. A 76, 031805(R) (2007)

    Article  ADS  Google Scholar 

  4. Lamata, L., Leibrandt, D. R., Chuang, I. L., Cirac, J. I., Lukin, M. D., Vuletic, V., Yelin, S. F.: Phys. Rev. Lett. 107, 030501 (2011)

    Article  ADS  Google Scholar 

  5. Ogden, C.D., Irish, E.K., Kim, M.S.: Phys. Rev. A 78, 063805 (2008)

    Article  ADS  Google Scholar 

  6. Li, P. B., Gu, Y., Gong, Q. H., Guo, G. C.: Phys. Rev. A 79, 042339 (2009)

    Article  ADS  Google Scholar 

  7. Yabu-uti, B. F. C., Roversi, J. A.: Quantum Inf. Process 12, 189 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  8. Cirac, J. I., Zoller, P., Kimble, H. J., Mabuchi, H.: Phys. Rev. Lett. 78, 3221 (1997)

    Article  ADS  Google Scholar 

  9. Hennessy, K., Badolato, A., Winger, M., Gerace, D., Atature, M., Gulde, S., Falt, S., Hu, E.L., Imamoglu, A.: Nature 445, 896 (2007)

    Article  ADS  Google Scholar 

  10. Khitrova, G., Gibbs, H.M., Kira, M., Kochs, W., Scherer, A.: Nat. Phys. 2, 81 (2006)

    Article  Google Scholar 

  11. Zhong, Z.R.: Opt. Commun. 283, 1972 (2010)

    Article  ADS  Google Scholar 

  12. Feng, X.L., Zhang, Z.M., Li, X.D.: Phys. Rev. Lett. 90, 217902 (2003)

    Article  ADS  Google Scholar 

  13. Pellizzari, T.: Phys. Rev. Lett. 79, 5242 (1997)

    Article  ADS  Google Scholar 

  14. Serafini, A., Mancini, S., Bose, S.: Phys. Rev. Lett. 96, 010503 (2006)

    Article  ADS  Google Scholar 

  15. Bellomo, B., Compagno, G., Lo Franco, R., Ridolfo, A., Savasta, S.: Phys. Scr. 2011, 014004 (2011)

    Article  Google Scholar 

  16. Greenberger, D.M., Horne, M., Zeilinger, A.: Bell’s Theorem, Quantum Theory, and Conceptions of the Universe. In: Kafatos, M. (ed.). Kluwer, Dordrecht (1989)

  17. Pan, J.W., Bouwmeester, D., Daniell, M., Weinfurter, H., Zeilinger, A.: Nature (London) 403, 515 (2000)

    Article  ADS  Google Scholar 

  18. Chen, R., Shen, L.: Phys. Lett. A 375, 3840 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  19. Li, W.-A., Wei, L.-F.: Opt. Express 20, 13440 (2012)

    Article  ADS  Google Scholar 

  20. Lu, X.-Y., Si, L.-G., Hao, X.-Y., Yang, X.: Phys. Rev. A 79, 052330 (2009)

    Article  ADS  Google Scholar 

  21. Duer, W., Vidal, G., Cirac, J. I.: Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  22. Kempe, J.: Phys. Rev. A 60, 910 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  23. Thapliyal, A.V.: ibid 59, 3336 (1999)

    ADS  MathSciNet  Google Scholar 

  24. Gottesman, D., Chuang, I. L.: Nature (London) 402, 390 (1999)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  26. Sanders, B. C.: Phys. Rev. A 45, 6811 (1992)

    Article  ADS  Google Scholar 

  27. Lund, A.P., Ralph, T.C., Haselgrove, H.L.: Phys. Rev. Lett. 100, 030503 (2008)

    Article  ADS  Google Scholar 

  28. An, N.B.: Phys. Lett. A 373, 1701 (2009)

    Article  ADS  Google Scholar 

  29. Marek, P., Fiurasek, J.: Phys. Rev. A 82, 014304 (2010)

    Article  ADS  Google Scholar 

  30. Jeong, H., An, N.B.: Phys. Rev. A 74, 022104 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  31. An, N. B.: Phys. Rev. A 69, 022315 (2004)

    Article  ADS  Google Scholar 

  32. Acin, A., Brus, D., Lewenstein, M., Sanpera, A.: Phys. Rev. Lett. 87, 040401 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  33. Bourennance, M., Eibl, M., Kurtsiefer, C., Gaertner, S., Weinfurter, H., Guhne, O., Hyllus, P., Brus, D., Lewenstein, M., Sanpera, A.: Phys. Rev. Lett. 92, 087902 (2004)

    Article  ADS  Google Scholar 

  34. Davidovich, L., Brune, M., Raimond, J. M., Haroche, S.: Phys. Rev. A 53, 1295 (1996)

    Article  ADS  Google Scholar 

  35. Fonseca Romero, K.M., Nemes, M.C., Peixoto, J.G., de Faria, A, Salgueiro, N., de Toledo Piza, A.F.R.: Phys. Rev. A 58, 3205 (1998)

    Article  ADS  Google Scholar 

  36. Wang, X., Sanders, B.C.: Phys. Rev. A 65, 012303 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  37. Zheng, S.B., Guo, G.C.: Phys. Rev. Lett. 85, 2392 (2000)

    Article  ADS  Google Scholar 

  38. Majer, J., et al.: Nature 449, 443 (2007)

    Article  ADS  Google Scholar 

  39. Gardiner, C., Zoller, P.: Quantum Noise. Springer, Berlin (2004)

    MATH  Google Scholar 

  40. Louisell, W.H., Marburger, W.H.: IEEE J. Quantum Electron. 3, 348 (1967)

    Article  ADS  Google Scholar 

  41. Hartmann, M.J., Prior, J., Clark, S.R., Plenio, M.B.: Phys. Rev. Lett. 102, 057202 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Fundamental Sciences, University of Tabriz, Tabriz, 51666-16471, Iran

    N. Behzadi

  2. Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, Tabriz, 51666-16471, Iran

    B. Ahansaz & S. Kazemi

Authors
  1. N. Behzadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Ahansaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Kazemi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Behzadi.

Appendix

Appendix

The solutions of (2) for \(\hat {a}_{2}(t)\), \(\hat {a}_{3}(t)\) and \(\hat {b}_{1}(t)\), \(\hat {b}_{2}(t)\) and \(\hat {b}_{3}(t)\) are given as follow:

$$ \hat{a}_{1}(t)=u_{11}(t)\hat{a}_{1}(0)+u_{12}(t)(\hat{a}_{2}(0)+\hat{a}_{3}(0))+v_{11}(t)\hat{b}_{1}(0)+v_{12}(t)(\hat{b}_{2}(0)+\hat{b}_{3}(0)), $$
(1)
$$ \hat{a}_{2}(t)=u_{11}(t)\hat{a}_{2}(0)+u_{12}(t)(\hat{a}_{1}(0)+\hat{a}_{3}(0))+v_{11}(t)\hat{b}_{2}(0)+v_{12}(t)(\hat{b}_{1}(0)+\hat{b}_{3}(0)), $$
(2)
$$ \hat{a}_{3}(t)=u_{11}(t)\hat{a}_{3}(0)+u_{12}(t)(\hat{a}_{1}(0)+\hat{a}_{2}(0))+v_{11}(t)\hat{b}_{3}(0)+v_{12}(t)(\hat{b}_{1}(0)+\hat{b}_{2}(0)), $$
(3)
$$ \hat{b}_{2}(t)=u_{21}(t)\hat{a}_{2}(0)+u_{22}(t)(\hat{a}_{1}(0)+\hat{a}_{3}(0))+v_{21}(t)\hat{b}_{2}(0)+v_{22}(t)(\hat{b}_{1}(0)+\hat{b}_{3}(0)), $$
(4)
$$ \hat{b}_{3}(t)=u_{21}(t)\hat{a}_{3}(0)+u_{22}(t)(\hat{a}_{1}(0)+\hat{a}_{2}(0))+v_{21}(t)\hat{b}_{3}(0)+v_{22}(t)(\hat{b}_{1}(0)+\hat{b}_{2}(0)), $$
(5)

where u 1j (t) and v 1j (t) for j = 1,2 are denoted as

$$\begin{array}{@{}rcl@{}} u_{11}(t)&=&\frac{e^{-i\omega_{c} t}}{3}\left( e^{-i(c-\frac{\Delta}{2})t}\left( cos\left( \frac{At}{2}\right)-\frac{i(2c+{\Delta})}{A}sin\left( \frac{At}{2}\right)\right)\right.\\ &&\left.+2e^{i(\frac{c+{\Delta}}{2})t}\left( cos\left( \frac{Bt}{2}\right)+\frac{i(c-{\Delta})}{B}sin\left( \frac{Bt}{2}\right)\right)\right)\\ u_{12}(t)&=&\frac{e^{-i\omega_{c} t}}{3}\left( e^{-i(c-\frac{\Delta}{2})t}\left( cos\left( \frac{At}{2}\right)-\frac{i(2c+{\Delta})}{A}sin\left( \frac{At}{2}\right)\right)\right.\\ &&\left.-e^{i(\frac{c+{\Delta}}{2})t}\left( cos\left( \frac{Bt}{2}\right)+\frac{i(c-{\Delta})}{B}sin\left( \frac{Bt}{2}\right)\right)\right) \\ v_{11}(t)&=&\frac{ie^{-i\omega_{c} t}}{6 g}\left( e^{-i(c-\frac{\Delta}{2})t}\left( -A+\frac{(2c+{\Delta})^{2}}{A}\right)sin\left( \frac{At}{2}\right)\right.\\ &&\left.-2e^{i(\frac{c+{\Delta}}{2})t}\left( B-\frac{(c-{\Delta})^{2}}{B}\right)sin\left( \frac{Bt}{2}\right)\right) \\ v_{12}(t)&=&\frac{ie^{-i\omega_{c} t}}{6 g}\left( e^{-i(c-\frac{\Delta}{2})t}\left( -A+\frac{(2c+{\Delta})^{2}}{A}\right)sin\left( \frac{At}{2}\right)\right.\\ &&\left.+e^{i(\frac{c+{\Delta}}{2})t}\left( B-\frac{(c-{\Delta})^{2}}{B}\right)sin\left( \frac{Bt}{2}\right)\right) \end{array} $$
(6)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Behzadi, N., Ahansaz, B. & Kazemi, S. Constructing Robust Entangled Coherent GHZ and W States via a Cavity QED System. Int J Theor Phys 55, 1577–1592 (2016). https://doi.org/10.1007/s10773-015-2796-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-015-2796-7

Keywords

Search

Navigation