Advertisement

Detection of Entanglement in Ultracold Lattice Gases

  • G. De Chiara
  • A. Sanpera
Article

Abstract

Probing non trivial magnetic ordering in quantum magnets realized with ultracold lattice gases demands detection methods with some spatial resolution built on it. Here we demonstrate that the Faraday matter-light interface provides an experimentally feasible tool to distinguish indubitably different quantum phases of a given many-body system in a non-demolishing way. We illustrate our approach by focussing on the Heisenberg chain for spin-1 bosons in the presence of a SU(2) symmetry breaking field. We explain how using the light signal obtained via homodyne detection one can reconstruct the phase diagram of the model. Further we show that the very same technique that provides a direct experimentally measurable signal of different order parameters can be extended to detect also the presence of multipartite entanglement in such systems.

Keywords

Optical lattices Entanglement 

References

  1. 1.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008) ADSCrossRefGoogle Scholar
  2. 2.
    M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen De, U. Sen, Adv. Phys. 56, 243 (2007) ADSCrossRefGoogle Scholar
  3. 3.
    J.L. Sørensen, J. Hald, E.S. Polzik, Phys. Rev. Lett. 80, 3487 (1998) ADSCrossRefGoogle Scholar
  4. 4.
    J.L. Sørensen, J. Hald, N. Jørgensen, E.S. Polzik, J. Mod. Opt. 44, 1917 (1997) ADSCrossRefGoogle Scholar
  5. 5.
    K. Eckert, O. Romero-Isart, M. Rodriguez, M. Lewenstein, E.S. Polzik, A. Sanpera, Nat. Phys. 4, 50 (2008) CrossRefGoogle Scholar
  6. 6.
    T. Roscilde, M. Rodriguez, K. Eckert, O. Romero-Isart, M. Lewenstein, E. Polzik, A. Sanpera, New J. Phys. 11, 055041 (2009) ADSCrossRefGoogle Scholar
  7. 7.
    G. De Chiara, O. Romero-Isart, A. Sanpera, Phys. Rev. A 83, 021604(R) (2011) ADSGoogle Scholar
  8. 8.
    O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    M. Wiesniak, V. Vedral, C. Brukner, New J. Phys. 7, 258 (2005) ADSCrossRefGoogle Scholar
  10. 10.
    P. Krammer, H. Kampermann, D. Bruß, R.A. Bertlmann, L.C. Kwek, C. Macchiavello, Phys. Rev. Lett. 103, 100502 (2009) MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    M. Cramer, M.B. Plenio, H. Wunderlich, Phys. Rev. Lett. 106, 020401 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    S.R. White, Phys. Rev. Lett. 69, 2863 (1992) ADSCrossRefGoogle Scholar
  13. 13.
    U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005) ADSCrossRefGoogle Scholar
  14. 14.
    G. De Chiara, M. Rizzi, D. Rossini, S. Montangero, J. Comput. Theor. Nanosci. 5, 1277 (2008) CrossRefGoogle Scholar
  15. 15.
    D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998) ADSCrossRefGoogle Scholar
  16. 16.
    A. Imambekov, M. Lukin, E. Demler, Phys. Rev. A 68, 063602 (2003) ADSCrossRefGoogle Scholar
  17. 17.
    M. Rizzi, D. Rossini, G. De Chiara, S. Montangero, R. Fazio, Phys. Rev. Lett. 95, 250404 (2005) ADSCrossRefGoogle Scholar
  18. 18.
    I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Phys. Rev. Lett. 59, 799 (1987) ADSCrossRefGoogle Scholar
  19. 19.
    A.V. Chubukov, Phys. Rev. B 43, 3337 (1991) ADSCrossRefGoogle Scholar
  20. 20.
    G. Fáth, J. Sólyom, Phys. Rev. B 51, 3620 (1995) ADSCrossRefGoogle Scholar
  21. 21.
    U. Schollwöck, Th. Jolicoeur, T. Garel, Phys. Rev. B 53, 3304 (1996) ADSCrossRefGoogle Scholar
  22. 22.
    K. Buchta, G. Fáth, Ö. Legeza, J. Sólyom, Phys. Rev. B 72, 054433 (2005) ADSCrossRefGoogle Scholar
  23. 23.
    A. Läuchli, G. Schmid, S. Trebst, Phys. Rev. B 74, 144426 (2006) ADSCrossRefGoogle Scholar
  24. 24.
    P. Reed, J. Phys. A 27, L69 (1994) ADSCrossRefGoogle Scholar
  25. 25.
    U. Schollwöck, J. Richter, D. Farnell, R. Bishop, Quantum Magnetism (Springer, Berlin, 2004) CrossRefGoogle Scholar
  26. 26.
    G. Fáth, J. Sólyom, Phys. Rev. B 44, 11836 (1991) ADSCrossRefGoogle Scholar
  27. 27.
    G. De Chiara, M. Lewenstein, A. Sanpera, Phys. Rev. B 84, 054451 (2011) ADSCrossRefGoogle Scholar
  28. 28.
    K. Rodriguez et al., Phys. Rev. Lett. 106, 105302 (2011) ADSCrossRefGoogle Scholar
  29. 29.
    Marcel den Nijs, Koos Rommelse. Phys. Rev. B 40, 4709 (1989) ADSCrossRefGoogle Scholar
  30. 30.
    G. Vitagliano, P. Hyllus, I.L. Egusquiza, G. Toth, arXiv:1104.3147

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Departament de Física, Informació i Processos QuànticsUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.ICREA, Instituciò Catalana de Recerca i Estudis AvançatsBarcelonaSpain

Personalised recommendations