The European Physical Journal B

, Volume 70, Issue 3, pp 377–396 | Cite as

Interferometry with independent Bose-Einstein condensates: parity as an EPR/Bell quantum variable

  • F. LaloëEmail author
  • W. J. Mullin
Mesoscopic and Nanoscale Systems


When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results ±1. With two interferometers and two BEC’s, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, significant violations of Bell inequalities are obtained. These violations do not tend to zero when the number N of particles increases, and can therefore be obtained with arbitrarily large systems, but a condition is that all particles should be detected. We discuss the general experimental requirements for observing such effects, the necessary detection of all particles in correlation, the role of the pixels of the CCD detectors, and that of the alignments of the interferometers in terms of matching of the wave fronts of the sources in the detection regions. Another scheme involving three interferometers and three BEC’s is discussed; it leads to Greenberger-Horne-Zeilinger (GHZ) sign contradictions, as in the usual GHZ case with three particles, but for an arbitrarily large number of them. Finally, generalizations of the Hardy impossibilities to an arbitrarily large number of particles are introduced. BEC’s provide a large versality for observing violations of local realism in a variety of experimental arrangements.


03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell’s inequalities, GHZ states, etc.) 03.75.Gg Entanglement and decoherence in Bose-Einstein condensates 42.50.Xa Optical tests of quantum theory 


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  1. 1.
    A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)zbMATHCrossRefADSGoogle Scholar
  2. 2.
    N. Bohr, Phys. Rev. 48, 696 (1935)zbMATHCrossRefADSGoogle Scholar
  3. 3.
    J.S. Bell, Physics 1, 195 (1964), reprinted in [4]Google Scholar
  4. 4.
    J.S. Bell, Speakable and unspeakable in quantum mechanics (Cambridge University Press, 1987)Google Scholar
  5. 5.
    S.J. Freedman, J.F. Clauser, Phys. Rev. Lett. 28, 938 (1972); S.J. Freedman, Thesis, University of California, Berkeley; J.F. Clauser, Phys. Rev. Lett. 36, 1223 (1976)CrossRefADSGoogle Scholar
  6. 6.
    E.S. Fry, R.C. Thompson, Phys. Rev. Lett. 37, 465 (1976)CrossRefADSGoogle Scholar
  7. 7.
    A. Aspect, P. Grangier, G. Roger, Phys. Rev. Lett. 47, 460 (1981); A. Aspect, P. Grangier, G. Roger, Phys. Rev. Lett. 49, 91 (1982)CrossRefADSGoogle Scholar
  8. 8.
    P.M. Pearle, Phys. Rev. D 2, 1418 (1970)CrossRefADSGoogle Scholar
  9. 9.
    J.F. Clauser, M.A. Horne, Phys. Rev. D 10, 526 (1974)CrossRefADSGoogle Scholar
  10. 10.
    J.F. Clauser, A. Shimony, Rep. on Progress in Phys. 41, 1883 (1978)ADSGoogle Scholar
  11. 11.
    F. Laloë, Bose-Einstein condensates and quantum non-locality, in Beyond the quantum, edited by T.M. Nieuwenhuizen, V. Spicka, B. Mehmadi, A. Khrennikov (World Scientific, 2007), e-print [arXiv:cond-mat/0611043], p. 35Google Scholar
  12. 12.
    N.D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    D.M. Greenberger, M.A. Horne, A. Zeilinger, in Bell theorem, quantum theory, and conceptions of the universe, edited by M. Kafatos (Kluwer, 1989), p. 74Google Scholar
  14. 14.
    D.M. Greenberger, M.A. Horne, A. Shimony, A. Zeilinger, Am. J. Phys. 58, 1131 (1990)CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    P. Drummond, Phys. Rev. Lett. 50, 1407 (1983)CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    F. Laloë, W.J. Mullin, Phys. Rev. Lett. 99, 150401 (2007)CrossRefADSGoogle Scholar
  17. 17.
    F. Laloë, W.J. Mullin, Phys. Rev. A 77, 022108 (2008)CrossRefADSGoogle Scholar
  18. 18.
    B. Saubamea, T.W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, C. Cohen-Tannoudji, Phys. Rev. Lett. 79, 3146 (1997)CrossRefADSGoogle Scholar
  19. 19.
    A. Robert, O. Sirjean, A. Browaeys, J. Poupard, S. Nowak, D. Bouron, C.I. Wesbrook, A. Aspect, Science 292, 461 (2001)CrossRefADSGoogle Scholar
  20. 20.
    J. Javanainen, SunMi Yoo, Phys. Rev. Lett. 76, 161 (1996)CrossRefADSGoogle Scholar
  21. 21.
    T. Wong, M.J. Collett, D.F. Walls, Phys. Rev. A 54, 3718 (1996)CrossRefADSGoogle Scholar
  22. 22.
    J.I. Cirac, C.W. Gardiner, M. Naraschewski, P. Zoller, Phys. Rev. A 54, R3714 (1996)CrossRefADSGoogle Scholar
  23. 23.
    C.J. Pethick, H. Smith, Bose-Einstein condensation in dilute gases (Cambridge University Press, 2002), Chap. 13Google Scholar
  24. 24.
    A. Dragan, P. Zin, Phys. Rev. A 76, 042124 (2007)CrossRefADSGoogle Scholar
  25. 25.
    M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn, W. Ketterle, Science 275, 637 (1997)CrossRefGoogle Scholar
  26. 26.
    A. Polkovnikov, E. Altman, E. Demler, Proc. Nat. Acad. Sci. USA 103, 6125 (2006)CrossRefADSGoogle Scholar
  27. 27.
    A. Polkovnikov, Eur. Phys. Lett. 78, 10006 (2007)CrossRefADSGoogle Scholar
  28. 28.
    J.A. Dunningham, K. Burnett, R. Roth, W.D. Phillips, New J. Phys. 8, 182 (2006)CrossRefADSGoogle Scholar
  29. 29.
    Y. Castin, J. Dalibard, Phys. Rev. A 55, 4330 (1997)CrossRefADSGoogle Scholar
  30. 30.
    A. Sinatra, Y. Castin, Eur. Phys. J. D 4, 247 (1998)CrossRefADSGoogle Scholar
  31. 31.
    M.J. Holland, K. Burnett, Phys. Rev. Lett. 71, 1355 (1993)CrossRefADSGoogle Scholar
  32. 32.
    J.P. Dowling, Phys. Rev. A 57, 4736 (1998)CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    J.A. Dunningham, K. Burnett, S.M. Barnett, Phys. Rev. Lett. 89, 150401 (2002)CrossRefADSGoogle Scholar
  34. 34.
    L. Pezze, A. Smerzi, Phys. Rev. A 73, 011801 (2006)CrossRefADSGoogle Scholar
  35. 35.
    L. Pezze, A. Semerzi, G. Khoury, J.F. Hodelin, D. Bouwmeester, Phys. Rev. Lett. 99, 223602 (2007)CrossRefADSGoogle Scholar
  36. 36.
    L. Pezze, A. Smerzi, Phys. Rev. Lett. 100, 073601 (2008)CrossRefADSGoogle Scholar
  37. 37.
    B. Yurke, D. Stoler, Phys. Rev. A 46, 2229 (1992)CrossRefADSMathSciNetGoogle Scholar
  38. 38.
    B. Yurke, D. Stoler, Phys. Rev. Lett. 68, 1251 (1992)CrossRefADSGoogle Scholar
  39. 39.
    J.D. Franson, Phys. Rev. Lett. 62, 2205 (1989)CrossRefADSGoogle Scholar
  40. 40.
    J.G. Rarity, P.R. Tapster, Phys. Rev. Lett. 64, 2495 (1990)CrossRefADSGoogle Scholar
  41. 41.
    P.W. Anderson, in The Lesson of Quantum Theory, edited by J. de Boer, E. Dahl, O. Ulfbeck (Elsevier, New York, 1986)Google Scholar
  42. 42.
    A.J. Leggett, F. Sols, Found. Phys. 21, 353 (1991)CrossRefADSGoogle Scholar
  43. 43.
    A.J. Leggett, in Bose-Einstein condensation, edited by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, 1995)Google Scholar
  44. 44.
    W.J. Mullin, R. Krotkov, F. Laloë, Phys. Rev. A 74, 023610 (2006)CrossRefADSGoogle Scholar
  45. 45.
    J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)CrossRefADSGoogle Scholar
  46. 46.
    L. Hardy, Phys. Lett. A 167, 17 (1992)CrossRefADSMathSciNetGoogle Scholar
  47. 47.
    L. Hardy, Phys. Rev. Lett. 71, 1665 (1993)zbMATHCrossRefADSMathSciNetGoogle Scholar
  48. 48.
    W.J. Mullin, F. Laloë, Phys. Rev. A 78, 0610605(R) (2008); W.J. Mullin, F. Laloë, J. Phys. Conf. Ser. 150, 032068 (2009)CrossRefGoogle Scholar
  49. 49.
    F. Laloë, Eur. Phys. J. D 33, 87 (2005)CrossRefADSGoogle Scholar
  50. 50.
    R. Glauber, in Quantum optics and electronics, Les Houches summer school 1964, edited by C. de Witt, A. Blandin, C. Cohen-Tannoudji (Gordon and Breach, 1965)Google Scholar
  51. 51.
    E.W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y.B. Band, M. Edwards, M. Doery, P.S. Julienne, K. Helmerson, S.L. Rolston, W.D. Phillips, Phys. Rev. Lett. 83, 3112 (1999)CrossRefADSGoogle Scholar
  52. 52.
    J.E. Simsarian, J. Denschlag, M. Edwards, C.W. Clark, L. Deng, E.W. Hagley, K. Helmerson, S.L. Rolston, W.D. Phillips, Phys. Rev. Lett. 85, 2040 (2000)CrossRefADSGoogle Scholar
  53. 53.
    A. Peres, Amer. J. Phys. 46, 645 (1978)CrossRefGoogle Scholar
  54. 54.
    Zhi Zhao, Yu-Ao Chen, An-Ning Zhang, Tao Yang, H.J. Briegel, Jian-Wei Pan, Nature 430, 54 (2004)CrossRefADSGoogle Scholar
  55. 55.
    J. Stenger, S. Inouye, A.P. Chikkatur, D.M. Stamper-Kurn, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999)CrossRefADSGoogle Scholar
  56. 56.
    Y.B. Ovchinnikov, J.H. Muller, M.R. Doery, E.J.D. Vredenbregt, K. Helmerson, S.L. Rolston, W.D. Phillips, Phys. Rev. Lett. 83, 284 (1999)CrossRefADSGoogle Scholar
  57. 57.
    J. Sebby-Strabley, B.L. Brown, M. Anderlini, P.J. Lee, W.D. Phillips, J.V. Porto, P.R. Johnson, Phys. Rev. Lett. 98, 200405 (2007)CrossRefADSGoogle Scholar
  58. 58.
    C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, S. Haroche, Nature 448, 889 (2007)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Laboratoire Kastler Brossel, ENS, UPMC, CNRSParisFrance
  2. 2.Department of PhysicsUniversity of MassachusettsAmherstUSA

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