International Journal of Theoretical Physics

, Volume 54, Issue 7, pp 2299–2311 | Cite as

Atomic and Photonic Entanglement Generation in n Coupled Atom-Cavity Systems



Based on two-photon Jaynes-Cummings Hamiltonian for the n coupled optical cavities each of them containing a single three level atom, the n-qubit and n-photonic state transfer between the corresponding atoms and cavities is investigated. In fact, we consider that the cavities are located at the nodes (vertices) of the complete network (graph) K n at which all of the nodes are connected, so that the cavities are interact with each other (via two photon exchange) completely. Then, quantum state transfer, photon transition between cavities and entanglement generations between n atoms are discussed. More clearly, by employing the consistency of number of photons and atomic excitations (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from 3 n dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times T at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength ξ between cavities.


Coupled cavities Two-photon Jaynes-Cummings Model (JCM) Complete network Hopping strength Three level atoms Generation of entanglement Excitation and photon transfer Fourier transform 


  1. 1.
    Bouwmeester, D. et al.: The Physics of Quantum Information. Springer, Berlin Heidelberg New York (2000)CrossRefMATHGoogle Scholar
  2. 2.
    Christandl, M., Datta, N., Ekert, A., Landahl, A.J.: Phys. Rev. Lett. 92, 187902 (2004)CrossRefADSGoogle Scholar
  3. 3.
    Christandl, M., Datta, N., Dorlas, T.C., Ekert, A., Kay, A., Landahl, A.J.: Phys. Rev. A. 71, 032312 (2005)CrossRefADSGoogle Scholar
  4. 4.
    Facer, C., Twamley, J., Cresser, J.: Phys. Rev. A 77, 012334 (2008)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Burgarth, D., Bose, S.: Phys. Rev. A 71, 052315 (2005)CrossRefADSGoogle Scholar
  6. 6.
    Burgarth, D., Bose, S.: New J. Phys. 7, 135 (2005)CrossRefADSGoogle Scholar
  7. 7.
    Yung, M.H., Bose, S.: Phys. Rev. A 71, 032310 (2005)CrossRefADSGoogle Scholar
  8. 8.
    Yung, M.H.: Phys. Rev. A 74, 030303 (2006)CrossRefADSGoogle Scholar
  9. 9.
    Jafarizadeh, M.A., Sufiani, R.: Phys. Rev. A 77, 022315 (2008)CrossRefADSGoogle Scholar
  10. 10.
    Jafarizadeh, M.A., et al.: J. Phys. A: Math. Theor. 41, 475302 (2008)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Jafarizadeh, M.A., et al.: J. Stat. Mech., 05014 (2011)Google Scholar
  12. 12.
    Turchette, Q.A., Hood, C.J., Lange, W., Mabuchi, H., Kimble, H.J.: Phys. Rev. Lett. 75, 4710 (1995)CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Brune, M., et al.: Phys. Rev. Lett. 77, 4887 (1996)CrossRefADSGoogle Scholar
  14. 14.
    Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Phys. Rev. Lett. 76, 4656 (1996)CrossRefADSGoogle Scholar
  15. 15.
    Biswas, A., Agarwal, G.S.: Phys. Rev. A 70, 022323 (2004)CrossRefADSGoogle Scholar
  16. 16.
    Cirac, J.I., Zoller, P., Kimble, H.J., Mabuchi, H.: Phys. Rev. Lett. 78, 3221 (1997)CrossRefADSGoogle Scholar
  17. 17.
    Alexanian, M., et al.: J. Mod. Opt. 45, 2519 (1998)CrossRefADSGoogle Scholar
  18. 18.
    Alexanian, M.: Phys. Rev. A 83, 023814 (2011)CrossRefADSGoogle Scholar
  19. 19.
    Alexanian, M.: arXiv:quant-ph:12034173 (2012)
  20. 20.
    Dong, Y.-L., et al.: Phys. Rev. A 85, 023833 (2012)CrossRefADSGoogle Scholar
  21. 21.
    Hardal, A.Ü.C., Mstecaplioglu, Ö.E.: J. Opt. Soc. Am. B 29, 1822–1828 (2012)CrossRefADSGoogle Scholar
  22. 22.
    Sufiani, R.: Quantum state transfer in atom-cavity systems with uncolored Cayley interacting networks. Int. J. Theor. Phys. (2014). doi: 10.1007/s10773-014-2213-7
  23. 23.
    Puri, R.R.: Mathematical Methods of Quantum Optics. Springer, Berlin Heidelberg New York (2001)CrossRefMATHGoogle Scholar
  24. 24.
    Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge, UK (1997)CrossRefGoogle Scholar
  25. 25.
    Hillery, M.: Acta physica slovaca. Rev. Tutor. 59, 1 (2009)Google Scholar
  26. 26.
    DellAnno, F., De Siena, S., Illuminati, F.: Phys. Rep. 428, 53 (2006)CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    Buzek, V., Hladky, B.: J. Mod. Opt. 40, 1309 (1998)CrossRefADSGoogle Scholar
  28. 28.
    Peres, A.: Phys. Rev. Lett. 77, 1413–1415 (1996)CrossRefADSMATHMathSciNetGoogle Scholar
  29. 29.
    Horodecki, M. et al.: Phys. Lett. A 223, 1–8 (1996)CrossRefADSMATHMathSciNetGoogle Scholar
  30. 30.
    Wootters, W.K.: Phys. Rev. Lett. 80, 2245–2248 (1998)CrossRefADSGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Theoretical Physics and AstrophysicsUniversity of TabrizTabrizIran
  2. 2.Physics Department, Faculty of ScienceAtatürk UniversityErzurumTurkey

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