Advertisement

The European Physical Journal D

, Volume 65, Issue 1–2, pp 33–42 | Cite as

Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator

  • G. Kónya
  • G. SzirmaiEmail author
  • P. Domokos
Regular Article Bose-Einstein condensates

Abstract

We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.

Keywords

Cavity Mode Quantum Phase Transition Matter Wave Entanglement Measure Ultracold Atom 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Domokos, H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    A.T. Black, H.W. Chan, V. Vuletić, Phys. Rev. Lett. 91, 203001 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    J. Javaloyes, M. Perrin, G.L. Lippi, A. Politi, Phys. Rev. A 70, 023405 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    J. Javaloyes, M. Perrin, A. Politi, Phys. Rev. E 78, 011108 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    J.K. Asbóth, P. Domokos, H. Ritsch, A. Vukics, Phys. Rev. A 72, 053417 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    D. Nagy, J.K. Asboth, P. Domokos, H. Ritsch, Europhys. Lett. 74, 254 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    T. Grießer, H. Ritsch, M. Hemmerling, Robb, Eur. Phys. J. D 58, 349 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    D. Nagy, G. Szirmai, P. Domokos, Eur. Phys. J. D 48, 127 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    A. Vukics, C. Maschler, H. Ritsch, New J. Phys. 9, 255 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    J. Keeling, M.J. Bhaseen, B.D. Simons, Phys. Rev. Lett. 105, 043001 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    S.F. Vidal, G. De Chiara, J. Larson, G. Morigi, Phys. Rev. A 81, 043407 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    J. Larson, J.P. Martikainen, Phys. Rev. A 82, 033606 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, Nature 464, 1301 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    D. Nagy, G. Kónya, G. Szirmai, P. Domokos, Phys. Rev. Lett. 104, 130401 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    R.H. Dicke, Phys. Rev. 93, 99 (1954)ADSCrossRefGoogle Scholar
  16. 16.
    F. Dimer, B. Estienne, A.S. Parkins, H.J. Carmichael, Phys. Rev. A 75, 013804 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    Y. Li, P. Zhang, Z.D. Wang, Eur. Phys. J. D 58, 379 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, T. Esslinger, Nature 450, 268 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, J. Reichel, Nature 450, 272 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    M.G. Moore, O. Zobay, P. Meystre, Phys. Rev. A 60, 1491 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    G. Szirmai, D. Nagy, P. Domokos, Phys. Rev. A 81, 043639 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    W. Chen, D.S. Goldbaum, M. Bhattacharya, P. Meystre, Phys. Rev. A 81, 053833 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    A.B. Bhattacherjee, J. Phys. B At. Mol. Opt. Phys. 43, 205301 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    F. Brennecke, S. Ritter, T. Donner, T. Esslinger, Science 322, 235 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    K.W. Murch, K.L. Moore, S. Gupta, D.M. Stamper-Kurn, Nature Phys. 4, 561 (2008)CrossRefGoogle Scholar
  26. 26.
    J.K. Asbóth, P. Domokos, H. Ritsch, Phys. Rev. A 70, 013414 (2004)ADSCrossRefGoogle Scholar
  27. 27.
    J.M. Zhang, F.C. Cui, D.L. Zhou, W.M. Liu, Phys. Rev. A 79, 033401 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    P. Horak, H. Ritsch, Phys. Rev. A 63, 023603 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    M. Lewenstein, L. You, Phys. Rev. Lett. 77, 3489 (1996)ADSCrossRefGoogle Scholar
  30. 30.
    Y. Castin, Bose-Einstein condensates in atomic gases: simple theoretical results, in Coherent atomic matter waves, edited by R. Kaiser, C. Westbrook, F. David (EDP Sciences and Springer-Verlag, 2001), pp. 1–136Google Scholar
  31. 31.
    M. Hillery, R.F. O’Connell, M. Scully, E. Wigner, Phys. Rep. 106, 121 (1984)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    S.L. Braunstein, P. van Loock, Rev. Mod. Phys. 77, 513 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    C. Emary, T. Brandes, Phys. Rev. E 67, 066203 (2003)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    N. Lambert, C. Emary, T. Brandes, Phys. Rev. Lett. 92, 073602 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    V. Bužek, M. Orszag, M. Roško, Phys. Rev. Lett. 94, 163601 (2005)ADSCrossRefGoogle Scholar
  36. 36.
    T. Barthel, M.C. Chung, U. Schollwöck, Phys. Rev. A 74, 022329 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    J. Vidal, S. Dusuel, T. Barthel, J. Stat. Mech. P01015 (2007)Google Scholar
  38. 38.
    S. Gopalakrishnan, B.L. Lev, P.M. Goldbart, Nature Phys. 5, 845 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    S. Gopalakrishnan, B.L. Lev, P.M. Goldbart, Phys. Rev. A 82, 043612 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Research Institute for Solid State Physics and OpticsBudapestHungary
  2. 2.ICFO-Institut de Ciències FotòniquesCastelldefels (Barcelona)Spain

Personalised recommendations