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Beyond Gross-Pitaevskii Mean-Field Theory

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Emergent Nonlinear Phenomena in Bose-Einstein Condensates

Part of the book series: Atomic, Optical, and Plasma Physics ((SSAOPP,volume 45))

A large number of effects related to the phenomenon of Bose-Einstein Condensation (BEC) can be understood in terms of lowest order mean-field theory, whereby the entire system is assumed to be condensed, with thermal and quantum fluctuations completely ignored [1]. Such a treatment leads to the Gross-Pitaevskii Equation (GPE) [2] used extensively throughout this book. Although this theory works remarkably well for a broad range of experimental parameters, a more complete treatment is required for understanding various experiments, including experiments with solitons and vortices. Such treatments should include the dynamical coupling of the condensate to the thermal cloud, the effect of dimensionality, the role of quantum fluctuations, and should also describe the critical regime, including the process of condensate formation.

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References

  1. C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge 2004); L.P. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford 2003) F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999) A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)

    Google Scholar 

  2. E.P. Gross, J. Math. Phys. 74, 195 (1963); L.P. Pitaevskii, Sov. Phys. JETP 13,451 (1961)

    Article  ADS  Google Scholar 

  3. A.L. Fetter, Ann. Phys. 70, 67 (1972)

    Article  ADS  Google Scholar 

  4. N.P. Proukakis, DPhil Thesis, University of Oxford (1997)

    Google Scholar 

  5. N.P. Proukakis, K. Burnett, J. Res. Natl. Inst. Stand. Technol. 101, 457 (1996)

    Google Scholar 

  6. S. Giorgini, Phys. Rev. A 57, 2949 (1998); ibid. 61, 033601 (2000)

    Article  ADS  Google Scholar 

  7. E. Zaremba, A. Griffin, T. Nikuni, Phys. Rev. A 57, 4695 (1998)

    Article  ADS  MATH  Google Scholar 

  8. A. Griffin, Phys. Rev. B 53, 9341 (1996)

    Article  ADS  Google Scholar 

  9. N.P. Proukakis, J. Phys. B 34, 4737 (2001)

    Article  ADS  Google Scholar 

  10. T. Nikuni, E. Zaremba, A. Griffin, Phys. Rev. Lett. 83, 10 (1999)

    Article  ADS  Google Scholar 

  11. M.J. Bijlsma, E. Zaremba, H.T.C. Stoof, Phys. Rev. A 62, 063609 (2000)

    Article  ADS  Google Scholar 

  12. R. Walser, J. Williams, J. Cooper, M. Holland, Phys. Rev. A 59, 3878 (1999)

    Article  ADS  Google Scholar 

  13. M.J. Davis, R.J. Ballagh, K. Burnett, J. Phys. B 34, 4487 (2001)

    Article  ADS  Google Scholar 

  14. A.L. Fetter, J.D. Walecka, Quantum theory of many-particle systems (McGraw Hill, New York, 1971); J.-P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge MA, 1986)

    Google Scholar 

  15. S.T. Beliaev, Sov. Phys. JETP 34, 289 (1958); ibid. 34 299 (1058)

    MathSciNet  Google Scholar 

  16. V.N. Popov, Sov. Phys. JETP 20, 1185 (1965). V.N. Popov, Functional Inte- grals and Collective Excitations (Cambridge University Press, 1987)

    Google Scholar 

  17. M. Bijlsma, H.T.C. Stoof, Phys. Rev. A 55, 498 (1997); H.T.C. Stoof, M. Bijlsma, M. Houbiers, J. Res. Natl. Inst. Stand. Technol. 101, 443 (1996)

    Article  ADS  Google Scholar 

  18. H.T.C. Stoof, Phys. Rev. Lett. 78, 768 (1997)

    Article  ADS  Google Scholar 

  19. N.P. Proukakis, K. Burnett, H.T.C. Stoof, Phys. Rev. A 57, 1230 (1998)

    Article  ADS  Google Scholar 

  20. N.P. Proukakis, K. Burnett, Philos. Trans. R. Soc. A 355, 2235 (1997)

    Article  ADS  Google Scholar 

  21. N.P. Proukakis, S.A. Morgan, S. Choi, K. Burnett, Phys. Rev. A 58, 2435 (1998)

    Article  ADS  Google Scholar 

  22. H. Shi, A. Griffin, Phys. Rep. 304, 1 (1998)

    Article  ADS  Google Scholar 

  23. S.A. Morgan, J. Phys. B 33, 3847 (2000); Phys. Rev. A 69, 023609 (2004); ibid. 72, 043609 (2005)

    Article  ADS  Google Scholar 

  24. K. Burnett, Proc. Int. School of Physics - Enrico Fermi, ed. M. Inguscio, S. Stringari, C. Wieman (IOS Press, Amsterdam, 1999)

    Google Scholar 

  25. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957); ibid. 106, 1135 (1957)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. N.N. Bogoliubov, J. Phys. USSR 11, 23 (1957)

    Google Scholar 

  27. C.W. Gardiner, Phys. Rev. A 56, 1414 (1997); M. Girardeau, A. Arnowitt, Phys. Rev. 113, 755 (1959); M. Girardeau, Phys. Rev. A 58, 775 (1998)

    Article  ADS  Google Scholar 

  28. C.W. Gardiner, P. Zoller, R.J. Ballagh, M.J. Davis, Phys. Rev. Lett. 79, 1793 (1997)

    Article  ADS  Google Scholar 

  29. Y. Castin, R. Dum, Phys. Rev. A 57, 3008 (1998)

    Article  ADS  Google Scholar 

  30. T.R. Kirkpatrick, J.R. Dorfman, Phys. Rev. A 28, 2576 (1983); J. Low Temp. Phys. 58, 301 (1985); ibid. 58, 399 (1985); U. Eckern, ibid. 54, 333 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  31. D.A.W Hutchinson, K. Burnett, R.J. Dodd, S.A. Morgan, M. Rusch, E. Zaremba, N.P. Proukakis, M. Edwards, C.W. Clark, J. Phys. B 33, 3825 (2000)

    Article  ADS  Google Scholar 

  32. D.A. Huse, E.D. Siggia, J. Low Temp. Phys. 46, 137 (1982); P. Dörre, H. Haug, D.B. Tran Thoai, ibid. 35, 465 (1979); D.H. Kobe, Ann. Phys. 45, 15 (1968); V.V. Goldman, I.F. Silvera, A.J. Leggett, Phys. Rev. B 24, 2870 (1981)

    Article  ADS  Google Scholar 

  33. V.I. Yukalov, H. Kleinert, Phys. Rev. A 73, 063612 (2006)

    Article  ADS  Google Scholar 

  34. D.A.W. Hutchinson, R.J. Dodd, K. Burnett, Phys. Rev. Lett. 81, 2198 (1998)

    Article  ADS  Google Scholar 

  35. J. Goldstone, Nuovo Cimento 19, 154 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  36. N.M. Hugenholtz, D. Pines, Phys. Rev. 116, 489 (1959); P.C. Hohenberg, P.C. Martin, Ann Phys. 34, 291 (1965); L.P. Kadanoff, G. Baym, Quantum Statistical Mechanics (New York: Benjamin, 1962)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. D.A.W. Hutchinson, E. Zaremba, A. Griffin, Phys. Rev. Lett. 78, 1842 (1997)

    Article  ADS  Google Scholar 

  38. M. Olshanii, L. Pricoupenko, Phys. Rev. Lett. 88, 010402 (2002)

    Article  ADS  Google Scholar 

  39. S.M.M. Virtanen, T.P. Simula, M.M. Salomaa, J. Phys: Condens. Matter 13, L819 (2001); C. Gies and D.A.W. Hutchinson, Phys. Rev. A 70, 043606 (2004); C. Gies, M.D. Lee, D.A.W. Hutchinson, J. Phys B 38, 1797 (2005)

    Article  ADS  Google Scholar 

  40. P. Tommasini, E.J.V. de Passos, M.O.C. Pires, A.F.R. de Toledo Piza, J. Phys: Condens. Matter 17, 3165 (2005); T. Kita, J. Phys. Soc. Jpn. 75, 044603 (2006)

    Article  ADS  Google Scholar 

  41. J. Wachter, Master’s Thesis, University of Boulder, Colorado (2000)

    Google Scholar 

  42. M. Imamovic-Tomasovic, A. Griffin, J. Low Temp. Phys. 122, 617 (2001)

    Article  Google Scholar 

  43. E. Zaremba, T. Nikuni, A. Griffin, J. Low Temp. Phys. 116, 277 (1999)

    Article  Google Scholar 

  44. J.R. Walser, J. Cooper, M. Holland, Phys. Rev. A 63, 013607 (2000); S.G. Bhongale, R. Walser, M.J. Holland, cond-mat/0203415 (2002); R. Walser, Opt. Commun. 243, 107 (2004); J. Wachter, R. Walser, J. Cooper, M. Holland, Phys. Rev. A 64, 053612 (2001)

    Article  ADS  Google Scholar 

  45. T. Köhler, K. Burnett, Phys. Rev. A 65, 033601 (2002); T. Köhler, T. Gasenzer, K. Burnett, Phys. Rev. A 67, 013601 (2003); T. Köhler, Phys. Rev. Lett. 89, 210404 (2002)

    Article  ADS  Google Scholar 

  46. M. Rusch, K. Burnett, Phys. Rev. A 59, 3851 (1999)

    Article  ADS  Google Scholar 

  47. D.S. Jin, M.R. Matthews, J.R. Enscher, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 78, 764 (1997); S.A. Morgan, M. Rusch, D.A.W. Hutchinson, K. Burnett, Phys. Rev. Lett. 91, 250403 (2001)

    Article  ADS  Google Scholar 

  48. M. Bijlsma, H.T.C Stoof, Phys. Rev. A 60, 3973 (1999); U. Al Khawaja, H.T.C. Stoof, Phys. Rev. A 62, 053602 (2000).

    Article  ADS  Google Scholar 

  49. B. Jackson, E. Zaremba, Phys. Rev. Lett. 88, 180402 (2002)

    Article  ADS  Google Scholar 

  50. D.W. Snoke, J.P. Wolfe, Phys. Rev. B 39, 4030 (1989) M. Holland, J. Williams, J. Cooper, Phys. Rev. A 55, 3670 (1997) D.V. Semikoz, I.I. Tkachev, Phys. Rev. Lett. 74, 3093 (1995) O.J. Luiten, M.W. Reynolds, J.T.M. Walraven, Phys. Rev. A 53, 381 (1996)

    Article  ADS  Google Scholar 

  51. B. Jackson, E. Zaremba, Phys. Rev. Lett. 87, 100404 (2001); ibid. 89, 150402 (2002); Phys. Rev. A 66, 033606 (2002); New. J. Phys. 5, 88 (2003)

    Article  ADS  Google Scholar 

  52. T. Nikuni, A Griffin, Phys. Rev. A 69, 023604 (2004); ibid. 63, 033608 (2001)

    Article  ADS  Google Scholar 

  53. J.E. Williams, E. Zaremba, B. Jackson, T. Nikuni, A. Griffin, Phys. Rev. Lett. 88,070401 (2002)

    Article  ADS  Google Scholar 

  54. S. Burger, K. Bongs, S. Dettmer, W. Etrmer, K. Sengstock, A. Sanpera, G.V. Shlyapnikov, M. Lewenstein, Phys. Rev. Lett. 83, 5198 (1999)

    Article  ADS  Google Scholar 

  55. B. Jackson, N.P. Proukakis, C.F. Barenghi, Phys. Rev. A 75, 051601(R)(2007)

    Article  ADS  Google Scholar 

  56. H.T.C. Stoof, J. Low Temp. Phys. 114, 11 (1999)

    Article  Google Scholar 

  57. P.O. Fedichev, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 80, 2269 (1998); P.O. Fedichev and G.V. Shlyapnikov, Phys. Rev. A 58, 3146 (1998); P.O. Fedichev and G.V. Shlyapnikov, Phys. Rev. A 60, R1779 (1999); P.O. Fedichev, A.E. Muryshev, G.V. Shlyapnikov, Phys. Rev. A 60, 3220 (1999)

    Article  ADS  Google Scholar 

  58. S. Sinha, A. Cherny, D. Kovrizhin, J. Brand, Phys. Rev. Lett. 96, 030406 (2006)

    Article  ADS  Google Scholar 

  59. H.T.C. Stoof, Dynamics: Models and Kinetic Methods for Non-Equilibrium Many-Body Systems, J. Karkheck (ed.) (Kluwer Academic Publishers, 1999)

    Google Scholar 

  60. H.T.C. Stoof, in Coherent Atomic Matter Waves, Proceedings of the Les Houches Summer School Session 72, 1999, ed. R. Kaiser et al. (Springer, Berlin 2001).

    Google Scholar 

  61. R.A. Duine, H.T.C. Stoof, Phys. Rev. A 65, 013603 (2001)

    Article  ADS  Google Scholar 

  62. A.A. Norrie, R.J. Ballagh, C.W. Gardiner, Phys. Rev. A 73, 043618 (2006)

    Article  ADS  Google Scholar 

  63. M.J. Steel, M.K. Olsen, L.I. Plimak, P.D. Drummond, S.M. Tan, M.J. Collett, D.F. Walls, R. Graham, Phys. Rev. A 58, 4824 (1998)

    Article  ADS  Google Scholar 

  64. D.G. Barci, E.S. Fraga, R.O. Ramos, Phys. Rev. Lett. 85, 479 (2000); D.G. Barci, E.S. Fraga, M. Gleiser, R.O. Ramos, Phys. A 317, 535 (2003); A.M. Rey, B.L. Hu, E. Calzetta, A. Roura, C.W. Clark, Phys. Rev. A 69, 033610 (2004); A.M. Rey, B.L. Hu, E. Calzetta, C.W. Clark, Phys. Rev. A 72, 023604 (2005); T. Gasenzer, J. Berges, M.G. Schmidt, M. Seco, Phys. Rev. A 72, 063604 (2005); K. Temme and T. Gasenzer, Phys. Rev. A 74, 053603 (2006)

    Article  ADS  Google Scholar 

  65. C.W. Gardiner, P. Zoller, Phys. Rev. A 55, 2902 (1997); D. Jaksch, C.W. Gardiner, P. Zoller, Phys. Rev. A 56, 575 (1997); C.W. Gardiner, P. Zoller, Phys. Rev. A 58, 536 (1998); D. Jaksch, C.W. Gardiner, K.M. Gheri, P. Zoller, Phys. Rev. A 58, 1450 (1998); C.W. Gardiner, P. Zoller, Phys. Rev. A 61, 033601 (2000); M.D. Lee, C.W. Gardiner, Phys. Rev. A 62, 033606 (2000); M.J. Davis, C.W. Gardiner, R.J. Ballagh, Phys. Rev. A 62, 063608 (1997)

    Article  ADS  Google Scholar 

  66. See, e.g., C.W. Gardiner, P. Zoller, Handbook of Stochastic Methods, 3rd ed. (Springer, Berlin, 2004)

    Google Scholar 

  67. C.W. Gardiner, M.D. Lee, R.J. Ballagh, M.J. Davis, P. Zoller, Phys. Rev. Lett. 81, 5266 (1998)

    Article  ADS  Google Scholar 

  68. H.J. Miesner, D.M. Stamper-Kurn, M.R. Andrews, D.S. Durfee, S. Inouye, W. Ketterle, Science 279, 1005 (1998)

    Article  ADS  Google Scholar 

  69. B.V. Svistunov, J. Mosc. Phys. Soc. 1, 373 (1991); Yu. Kagan, B.V. Svistunov, G. Shlyapnikov, Sov. Phys. JETP 75, 387 (1992); Yu. Kagan, B.V. Svistunov, Sov. Phys. JETP 78, 187 (1994); Yu. Kagan, B.V. Svistunov, Phys. Rev. Lett. 79,3331 (1997) Sov. Phys. JETP 75, 387 (1992)

    Google Scholar 

  70. K. Damle, S.N. Majumdar, S. Sachdev, Phys. Rev. A 54, 5037 (1996)

    Article  ADS  Google Scholar 

  71. R.J. Marshall, G.H.C. New, K. Burnett, S. Choi, Phys. Rev. A 59, 2085 (1999)

    Article  ADS  Google Scholar 

  72. N.G. Berloff, B.V. Svistunov, Phys. Rev. A 66, 013603 (2002)

    Article  ADS  Google Scholar 

  73. M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. Lett. 87, 160402 (2001)

    Article  ADS  Google Scholar 

  74. M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. A 66, 053618 (2001); P.B. Blakie, M.J. Davis, Phys. Rev. A 72, 063608 (2005); M.J. Davis P.B. Blakie, Phys. Rev. Lett. 96, 060404 (2006); T.P. Simula P.B. Blakie, Phys. Rev. Lett. 96, 020404 (2006)

    Article  ADS  Google Scholar 

  75. K. Goral, M. Gajda, K. Rzazewski, Phys. Rev. A 66, 051602 (2002); H. Schmidt, K. Goral, F. Floegel, M. Gajda, K. Rzazewski, J. Opt. B 5, S96 (2003); M. Leadbeater, T. Winiecki, C.S. Adams, J. Phys. B 36, L143 (2003)

    Article  ADS  Google Scholar 

  76. A. Sinatra, C. Lobo, Y. Castin, Phys. Rev. Lett. 87, 210404 (2001); A. Sinatra, C. Lobo, and Y. Castin, J. Phys. B 35, 3599 (2002)

    Article  ADS  Google Scholar 

  77. R.G. Scott, D.A.W. Hutchinson, C.W. Gardiner, Phys. Rev. A 74, 053605 (2006); A.A. Norrie, R.J. Ballagh, C.W. Gardiner, A.S. Bradley, Phys. Rev. A 73, 043618 (2006); S. Wüster, B.J. Dabrowska-Wüster, A.S. Bradley, M.J. Davis, P.B. Blakie, J.J. Hope, and C.M. Savage, Phys. Rev. A 75, 043611 (2007)

    Article  ADS  Google Scholar 

  78. A. Polkovnikov, Phys. Rev. A 68, 033609 (2003); ibid. 68, 053604 (2003)

    Article  ADS  Google Scholar 

  79. P.D. Drummond, J.F. Corney, Phys. Rev. A 60, R2661 (1999)

    Article  ADS  Google Scholar 

  80. P. Deuar, P.D. Drummond, Phys. Rev. Lett. 98, 120402 (2007) P.D. Drummond, P. Deuar, J. Opt. B 5, S281 (2003)

    Article  ADS  Google Scholar 

  81. H.T.C. Stoof, M.J. Bijlsma, J. Low Temp. Phys. 124, 431 (2001)

    Article  Google Scholar 

  82. D.M. Stamper-Kurn, H.-J. Miesner, A.P. Chikatur, S. Inouye, W. Ketterle, Phys. Rev. Lett. 81, 2194 (1998)

    Article  ADS  Google Scholar 

  83. N.P. Proukakis, J. Schmiedmayer, H.T.C. Stoof, Phys. Rev. A 73, 053603 (2006); N.P. Proukakis, Phys. Rev. A 74, 053617 (2006); Las. Phys. 13, 527 (2003)

    Article  ADS  Google Scholar 

  84. R.A Duine, B.W.A. Leurs, and H.T.C. Stoof, Phys. Rev. A 69, 053623 (2004)

    Article  ADS  Google Scholar 

  85. L.P. Pitaevskii, Sov. Phys. JETP 35, 282 (1959)

    MathSciNet  Google Scholar 

  86. S. Choi, S.A. Morgan, K. Burnett, Phys. Rev. A 57, 4057 (1998)

    Article  ADS  Google Scholar 

  87. M. Tsubota, K. Kasamatsu, M. Ueda, Phys. Rev. A 65, 023603 (2002); M. Tsubota, K. Kasamatsu, M. Ueda, Phys. Rev. A 67, 033610 (2003) N.P. Proukakis, N.G. Parker, C.F. Barenghi, C.S. Adams, Phys. Rev. Lett. 93,130408 (2004)

    Article  ADS  Google Scholar 

  88. C.W. Gardiner, J.R. Anglin, T.I.A. Fudge, J. Phys. B 35, 1555 (2002); C.W. Gardiner, M.J. Davis, J. Phys. B 36, 4731 (2003); A.S. Bradley, P.B. Blakie, C.W. Gardiner, J. Phys. B 38, 4259 (2005)

    Google Scholar 

  89. A.A. Penckwitt, R.J. Ballagh, C.W. Gardiner, Phys. Rev. Lett. 89, 260402 (2002)

    Article  ADS  Google Scholar 

  90. See, e.g., S. Richard, F. Gerbier, J.H. Thywiseen, M. Hugbart, P. Bouyer, A. Aspect, Phys. Rev. Lett. 91, 010405 (2003); Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J.B. Dalibard, Nature 441, 1118 (2006) and references therein

    Article  ADS  Google Scholar 

  91. D.S. Petrov, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 85, 3745 (2000); D.S. Petrov, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 87, 050404 (2001); D.L. Luxat and A. Griffin, Phys. Rev. A 67, 043603 (2003); C. Mora, Y. Castin, Phys. Rev. A 67, 053615 (2003)

    Article  ADS  Google Scholar 

  92. J.O. Andersen, U. Al Khawaja, H.T.C. Stoof, Phys. Rev. Lett. 88, 070407 (2002); U. Al Khawaja, J.O. Andersen, N.P. Proukakis, H.T.C. Stoof, Phys. Rev. A 66, 013615 (2002); U. Al Khawaja, J.O. Andersen, N.P. Proukakis, H.T.C. Stoof, Phys. Rev. A 66, 059902(E) (2002); U. Al Khawaja, N.P. Proukakis, J.O. Andersen, M.W.J. Romans, H.T.C. Stoof, Phys. Rev. A 68, 043603 (2003); N.P. Proukakis, Phys. Rev. A 73, 023605 (2006)

    Article  ADS  Google Scholar 

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  1. Newcastle University, NE1 7RU, Newcastle-upon-Tyne, UK

    N. P. Proukakis

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  1. University of Massachusetts, Amherst, MA, 01003-4515, USA

    Panayotis G. Kevrekidis

  2. University of Athens, Athens, 15784, Greece

    Dimitri J. Frantzeskakis

  3. San Diego State University, San Diego, CA, 92182-7720, USA

    Ricardo Carretero-González

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Proukakis, N.P. (2008). Beyond Gross-Pitaevskii Mean-Field Theory. In: Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R. (eds) Emergent Nonlinear Phenomena in Bose-Einstein Condensates. Atomic, Optical, and Plasma Physics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73591-5_18

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