Vortices in Bose-Einstein Condensates: Theory

  • N. G. Parker
  • B. Jackson
  • A. M. Martin
  • C. S. Adams

Vortices are pervasive in nature, representing the breakdown of laminar fluid flow and hence playing a key role in turbulence. The fluid rotation associated with a vortex can be parameterized by the circulation Γ = ∮ dr · v(r) about the vortex, where v(r) is the fluid velocity field. While classical vortices can take any value of circulation, superfluids are irrotational, and any rotation or angular momentum is constrained to occur through vortices with quantized circulation. Quantized vortices also play a key role in the dissipation of transport in superfluids. In BECs quantized vortices have been observed in several forms, including single vortices [1, 2], vortex lattices [3–6] (see also Part VII), and vortex pairs and rings [7–9]. The recent observation of quantized vortices in a fermionic gas was taken as a clear signature of the underlying condensation and superfluidity of fermion pairs [10]. In addition to BECs, quantized vortices also occur in superfluid helium [11, 12], nonlinear optics, and type-II superconductors [13].

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References

  1. 1.
    M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 83, 2498 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    B.P. Anderson, P.C. Haljan, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 85, 2857 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Phys. Rev. Lett. 84, 806 (2000)ADSCrossRefGoogle Scholar
  4. 4.
    J.R. Abo-Shaeer, C. Raman, J.M. Vogels, W. Ketterle, Science 292, 476 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    E. Hodby, C. Hechenblaikner, S.A. Hopkins, O.M. Maragò, C.J. Foot, Phys. Rev. Lett. 88, 010405 (2002)ADSCrossRefGoogle Scholar
  6. 6.
    C. Raman, J.R. Abo-Shaeer, J.M. Vogels, K. Xu, W. Ketterle, Phys. Rev. Lett. 87, 210402 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    B.P. Anderson, P.C. Haljan, C.A. Regal, D.L. Feder, L.A. Collins, C.W. Clark, E.A. Cornell, Phys. Rev. Lett. 86, 2926 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    Z. Dutton, M. Budde, C. Slowe, L.V. Hau, Science 293, 663 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    S. Inouye, S. Gupta, T. Rosenband, A.P. Chikkatur, A. Görlitz, T.L. Gustavson, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 87, 080402 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, Nature 435, 1047 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    R.J. Donnelly, Quantized vortices in Helium II (Cambridge University Press, Cambridge, 1991)Google Scholar
  12. 12.
    C.F. Barenghi, R.J. Donnelly, W.F. Vinen (ed.), Quantized Vortex Dynamics and Superfluid Turbulence (Springer, Berlin Heidelberg New York, 2001)Google Scholar
  13. 13.
    D.R. Tilley, J. Tilley, Superfluidity and Superconductivity (IOP, Bristol, 1990)Google Scholar
  14. 14.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    A.L. Fetter, A.A. Svidzinsky, J. Phys.: Condens. Matter 13, R135 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    F. Dalfovo, S. Stringari, Phys. Rev. A 53, 2477 (1996)ADSCrossRefGoogle Scholar
  17. 17.
    N.K. Wilkin, J.M.F. Gunn, R.A. Smith, Phys. Rev. Lett. 80, 2265 (1998)ADSCrossRefGoogle Scholar
  18. 18.
    H. Saito, M. Ueda, Phys. Rev. A 69, 013604 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    E. Lundh, A. Collin, K.-A. Suominen, Phys. Rev. Lett. 92, 070401 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    G.M. Kavoulakis, A.D. Jackson, G. Baym, Phys. Rev. A 70, 043603 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    S.M.M. Virtanen, T.P. Simula, M.M. Salomaa, Phys. Rev. Lett. 86, 2704 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    C.W. Gardiner, J.R. Anglin, T.I.A. Fudge, J. Phys. B 35, 1555 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    A.A. Penckwitt, R.J. Ballagh, C.W. Gardiner, Phys. Rev. Lett. 89, 260402 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    R.A. Duine, B.W.A. Leurs, H.T.C. Stoof, Phys. Rev. A 69, 053623 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    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)ADSCrossRefGoogle Scholar
  26. 26.
    M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. A 66, 053618 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    C. Lobo, A. Sinatra, Y. Castin, Phys. Rev. Lett. 92, 020403 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    T.P. Simula, P.B. Blakie, Phys. Rev. Lett. 96, 020404 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    M. Tsubota, K. Kasamatsu, M. Ueda, Phys. Rev. A 65, 023603 (2002)ADSCrossRefGoogle Scholar
  30. 30.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge, 2002)Google Scholar
  31. 31.
    A. Minguzzi, S. Succi, F. Toschi, M. P. Tosi, P. Vignolo, Phys. Rep. 395, 223 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    D.A. Butts, D.S. Rokshar, Nature 397, 327 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    E. Lundh, Phys. Rev. A 65, 043604 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    P.C. Haljan, I. Coddington, P. Engels, E.A. Cornell, Phys. Rev. Lett. 87, 210403 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    M. Möttönen, T. Mizushima, T. Isoshima, M.M. Salomaa, K. Machida, Phys. Rev. A 68, 023611 (2003)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Shin, M. Saba, A. Schirotzek, T.A. Pasquini, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 93, 160406 (2004)ADSCrossRefGoogle Scholar
  37. 37.
    H. Pu, C.K. Law, J.H. Eberly, N.P. Bigelow, Phys. Rev. Lett. 59, 1533 (1999)ADSGoogle Scholar
  38. 38.
    T.P. Simula, S.M.M. Virtanen, M.M. Salomaa, Phys. Rev. A 65, 033614 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    C.A. Jones, P.H. Roberts, J. Phys. A 15, 2599 (1982)ADSCrossRefGoogle Scholar
  40. 40.
    C.A. Jones, S.J. Putterman, P.H. Roberts, J. Phys. A 19, 2991 (1986)ADSCrossRefGoogle Scholar
  41. 41.
    A.E. Leanhardt, Y. Shin, D. Kielpinski, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 90, 140403 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    K. Kasamatsu, M. Tsubota, M. Ueda, Phys. Rev. Lett. 93, 250406 (2004)ADSCrossRefGoogle Scholar
  43. 43.
    J. Ruostekoski and J.R. Anglin, Phys. Rev. Lett. 86, 003934 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    J. Ruostekoski, J.R. Anglin, Phys. Rev. Lett. 91, 190402 (2003)ADSCrossRefGoogle Scholar
  45. 45.
    N.G. Parker, N.P. Proukakis, C.F. Barenghi, C.S. Adams, Phys. Rev. Lett. 92, 160403 (2004)ADSCrossRefGoogle Scholar
  46. 46.
    P. Nozieres, D. Pines, The Theory of Quantum Liquids (Perseus, New York, 1999)Google Scholar
  47. 47.
    E. Lundh, C.J. Pethick, H. Smith, Phys. Rev. A 55, 2126 (1997)ADSCrossRefGoogle Scholar
  48. 48.
    D.S. Rokhsar, Phys. Rev. Lett. 79, 2164 (1997)ADSCrossRefGoogle Scholar
  49. 49.
    E. Lundh, J.P. Martikainen, K. A. Suominen, Phys. Rev. A 67, 063604 (2003)ADSCrossRefGoogle Scholar
  50. 50.
    N.G. Parker, C.S. Adams, Phys. Rev. Lett. 95, 145301 (2005); J. Phys. B 39, 43 (2006)ADSCrossRefGoogle Scholar
  51. 51.
    S. Stringari, Phys. Rev. Lett. 77, 2360 (1996)ADSCrossRefGoogle Scholar
  52. 52.
    A. Recati, F. Zambelli, S. Stringari, Phys. Rev. Lett. 86, 377 (2001)ADSCrossRefGoogle Scholar
  53. 53.
    S. Sinha, Y. Castin, Phys. Rev. Lett. 87, 190402 (2001)ADSCrossRefGoogle Scholar
  54. 54.
    N.G. Parker, R.M.W. van Bijnen, A.M. Martin, Phys. Rev. A 73, 061603(R) (2006)ADSCrossRefGoogle Scholar
  55. 55.
    K.W. Madison, F. Chevy, V. Bretin, J. Dalibard, Phys. Rev. Lett. 86, 4443 (2001)ADSCrossRefGoogle Scholar
  56. 56.
    J.E. Williams, E. Zaremba, B. Jackson, T. Nikuni, A. Griffin, Phys. Rev. Lett. 88, 070401 (2002)ADSCrossRefGoogle Scholar
  57. 57.
    F. Dalfovo and S. Stringari, Phys. Rev. A 63, 011601(R) (2001)ADSCrossRefGoogle Scholar
  58. 58.
    T. Frisch, Y. Pomeau, S. Rica, Phys. Rev. Lett. 69, 1644 (1992)ADSCrossRefGoogle Scholar
  59. 59.
    T. Winiecki, J.F. McCann, C. S. Adams, Phys. Rev. Lett. 82, 5186 (1999)ADSCrossRefGoogle Scholar
  60. 60.
    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. Lett. 80, 3903 (1998)ADSCrossRefGoogle Scholar
  61. 61.
    C. Raman, M. Köhl, R. Onofrio, D.S. Durfee, C.E. Kuklewicz, Z. Hadzibabic, W. Ketterle, Phys. Rev. Lett. 83, 2502 (1999)ADSCrossRefGoogle Scholar
  62. 62.
    R. Onofrio, C. Raman, J.M. Vogels, J.R. Abo-Shaeer, A.P. Chikkatur, W. Ketterle, Phys. Rev. Lett. 85, 2228 (2000)ADSCrossRefGoogle Scholar
  63. 63.
    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. A 61, 051603(R) (2000)ADSCrossRefGoogle Scholar
  64. 64.
    B.M. Caradoc-Davies, R.J. Ballagh, K. Burnett, Phys. Rev. Lett. 83, 895 (1999)ADSCrossRefGoogle Scholar
  65. 65.
    J.E. Williams, M.J. Holland, Nature 401, 568 (1999)ADSCrossRefGoogle Scholar
  66. 66.
    A.E. Leanhardt, A. Görlitz, A. Chikkatur, D. Kielpinski, Y. Shin, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 89, 190403 (2002)ADSCrossRefGoogle Scholar
  67. 67.
    N.S. Ginsberg, J. Brand, L.V. Hau, Phys. Rev. Lett. 94, 040403 (2005)ADSCrossRefGoogle Scholar
  68. 68.
    S. Komineas, N. Papanicolaou, Phys. Rev. A 68, 043617 (2003)ADSCrossRefGoogle Scholar
  69. 69.
    R.G. Scott, A.M. Martin, T.M. Fromhold, F.W. Sheard, Phys. Rev. Lett. 95, 073201 (2005)ADSCrossRefGoogle Scholar
  70. 70.
    R.G. Scott, A.M. Martin, S. Bujkiewicz, T. M. Fromhold, N. Malossi, O. Morsch, M. Cristiani, E. Arimondo, Phys. Rev. A 69, 033605 (2004)ADSCrossRefGoogle Scholar
  71. 71.
    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. A 60, 4882 (1999)ADSCrossRefGoogle Scholar
  72. 72.
    N.G. Berloff, C.F. Barenghi, Phys. Rev. Lett. 93, 090401 (2004)ADSCrossRefGoogle Scholar
  73. 73.
    J. Ruostekoski, Z. Dutton, Phys. Rev. A 70, 063626 (2005)ADSCrossRefGoogle Scholar
  74. 74.
    L.C. Crasovan, V.M. Pérez-García, I. Danaila, D. Mihalache, L. Torner, Phys. Rev. A 70, 033605 (2004)ADSCrossRefGoogle Scholar
  75. 75.
    T.P. Simula, P.B. Blakie, Phys. Rev. Lett. 96, 020404 (2006)ADSCrossRefGoogle Scholar
  76. 76.
    Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006)ADSCrossRefGoogle Scholar
  77. 77.
    M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. Lett. 66, 053618 (2002)ADSGoogle Scholar
  78. 78.
    N.G. Berloff, B.V. Svistunov, Phys. Rev. A 66, 013603 (2002)ADSCrossRefGoogle Scholar
  79. 79.
    H. Lamb, Hydrodynamics (Cambridge University Press, 1932)Google Scholar
  80. 80.
    M. Tsubota, T. Araki, S.K. Nemirovskii, Phys. Rev. B 62, 11751 (2000)ADSCrossRefGoogle Scholar
  81. 81.
    K.W. Schwarz, Phys. Rev. B 31, 5782 (1985)ADSCrossRefGoogle Scholar
  82. 82.
    J. Koplik, H. Levine, Phys. Rev. Lett. 71, 1375 (1993)ADSCrossRefGoogle Scholar
  83. 83.
    M. Leadbeater, T. Winiecki, D.C. Samuels, C.F. Barenghi, C.S. Adams, Phys. Rev. Lett. 86, 1410 (2001)ADSCrossRefGoogle Scholar
  84. 84.
    M. Leadbeater, D.C. Samuels, C.F. Barenghi, C.S. Adams, Phys. Rev. A 67, 015601 (2003)ADSCrossRefGoogle Scholar
  85. 85.
    W. Thomson (Lord Kelvin), Philos. Mag. 10, 155 (1880)Google Scholar
  86. 86.
    G.W. Rayfield, F. Reif, Phys. Rev. 136, A1194 (1964)ADSCrossRefGoogle Scholar
  87. 87.
    A.A. Svidzinsky, A.L. Fetter, Phys. Rev. Lett. 84, 5919 (2000)ADSCrossRefGoogle Scholar
  88. 88.
    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. A 61, 013604 (2000)ADSCrossRefGoogle Scholar
  89. 89.
    E. Lundh, P. Ao, Phys. Rev. A 61, 063612 (2000)ADSCrossRefGoogle Scholar
  90. 90.
    S.A. McGee, M.J. Holland, Phys. Rev. A 63, 043608 (2001)ADSCrossRefGoogle Scholar
  91. 91.
    J.J. García-Ripoll, V.M. Pérez-García, Phys. Rev. A 63, 041603 (2001)ADSCrossRefGoogle Scholar
  92. 92.
    J.J. García-Ripoll, V.M. Pérez-García, Phys. Rev. A 64, 053611 (2001)ADSCrossRefGoogle Scholar
  93. 93.
    A. Aftalion, T. Riviere, Phys. Rev. A 64, 043611 (2001)ADSCrossRefGoogle Scholar
  94. 94.
    P. Rosenbusch, V. Bretin, J. Dalibard, Phys. Rev. Lett. 89, 200403 (2002)ADSCrossRefGoogle Scholar
  95. 95.
    V. Bretin, P. Rosenbusch, F. Chevy, G.V. Shlyapnikov, J. Dalibard, Phys. Rev. Lett. 90, 100403 (2003)ADSCrossRefGoogle Scholar
  96. 96.
    A.L. Fetter, Phys. Rev. A 69, 043617 (2004)ADSCrossRefGoogle Scholar
  97. 97.
    P.O. Fedichev, G.V. Shylapnikov, Phys. Rev. A 60, R1779 (1999)ADSCrossRefGoogle Scholar
  98. 98.
    J.R. Abo-Shaeer, C. Raman, W. Ketterle, Phys. Rev. Lett. 88, 070409 (2002)ADSCrossRefGoogle Scholar
  99. 99.
    S.I. Davis, P.C. Hendry, P.V.E. McClintock, Physica B 280, 43 (2000)ADSCrossRefGoogle Scholar
  100. 100.
    D.P. Arovas, J.A. Freire, Phys. Rev. B 55, 3104 (1997)ADSCrossRefGoogle Scholar
  101. 101.
    W.F. Vinen, Phys. Rev. B 61, 1410 (2000)ADSCrossRefGoogle Scholar
  102. 102.
    E. Lundh, P. Ao, Phys. Rev. A 61, 063612 (2000)ADSCrossRefGoogle Scholar
  103. 103.
    L.M. Pismen, Vortices in Nonlinear Fields (Clarendon, Oxford, 1999)MATHGoogle Scholar
  104. 104.
    C.F. Barenghi, N.G. Parker, N.P. Proukakis, C.S. Adams, J. Low. Temp. Phys. 138,629 (2005)ADSCrossRefGoogle Scholar
  105. 105.
    N.G. Berloff, Phys. Rev. A 69, 053601 (2004)ADSCrossRefGoogle Scholar
  106. 106.
    B.M. Caradoc-Davies, R.J. Ballagh, P.B. Blakie, Phys. Rev. A 62, 011602 (2000)ADSCrossRefGoogle Scholar
  107. 107.
    A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, T. Pfau, Phys. Rev. Lett. 94, 160401 (2005)ADSCrossRefGoogle Scholar
  108. 108.
    M. Marinescu, L. You, Phys. Rev. Lett. 81, 4596 (1998)ADSCrossRefGoogle Scholar
  109. 109.
    S. Yi, L. You, Phys. Rev. A 61, 041604 (2000)ADSCrossRefGoogle Scholar
  110. 110.
    K. Góral, K. Rza Żewski, T. Pfau, Phys. Rev. A 61, 051601 (2000)ADSCrossRefGoogle Scholar
  111. 111.
    S. Yi, H. Pu, Phys. Rev. A 73, 061602(R) (2006)ADSCrossRefGoogle Scholar
  112. 112.
    G. Oritz, D.M. Ceperley, Phys. Rev. Lett. 75, 4642 (1995)ADSCrossRefGoogle Scholar
  113. 113.
    M. Sadd, G.V. Chester, L. Reatto, Phys. Rev. Lett. 79, 2490 (1997)ADSCrossRefGoogle Scholar
  114. 114.
    N. G. Berloff, P.H. Roberts, J. Phys. A 32, 5611 (1999)MATHMathSciNetADSCrossRefGoogle Scholar
  115. 115.
    F. Dalfovo, Phys. Rev. B 46, 5482 (1992)ADSCrossRefGoogle Scholar
  116. 116.
    J. Stuhler, A. Griesmaier, T. Koch, M. Fattori, T. Pfau, S. Giovanazzi, P. Pedri, L. Santos, Phys. Rev. Lett. 95, 150406 (2005)ADSCrossRefGoogle Scholar
  117. 117.
    D.H.J. O’Dell, C. Eberlein, Phys. Rev. A 75, 013604 (2007)ADSCrossRefGoogle Scholar
  118. 118.
    D.H.J. O’Dell, S. Giovanazzi, C. Eberlein, Phys. Rev. Lett. 92, 250401 (2004)CrossRefGoogle Scholar
  119. 119.
    C. Eberlein, S. Giovanazzi, D.H.J. O’Dell, Phys. Rev. A 71, 033618 (2005)ADSCrossRefGoogle Scholar
  120. 120.
    R.M.W. van Bijnen, D.H.J. O’Dell, N.G. Parker, A.M. Martin, Phys. Rev. Lett. 98, 150401 (2007)ADSCrossRefGoogle Scholar
  121. 121.
    C. Barceló, S. Liberati, M. Visser, Living Rev. Rel. 8, 12 (2005)Google Scholar
  122. 122.
    W.G. Unruh, Phys. Rev. Lett. 46, 1351 (1981)ADSCrossRefGoogle Scholar
  123. 123.
    W.G. Unruh, Phys. Rev. D 27, 2827 (1995)MathSciNetADSCrossRefGoogle Scholar
  124. 124.
    C. Barceló, S. Liberati, M. Visser, Class. Quant. Gav. 18, 1137 (2001)MATHADSCrossRefGoogle Scholar
  125. 125.
    S.W. Hawking, Nature 248, 30 (1974)ADSCrossRefGoogle Scholar
  126. 126.
    S.W. Hawking, Commun. Math. Phys. 43, 199 (1975)MathSciNetADSCrossRefGoogle Scholar
  127. 127.
    J.D. Bekenstein, M. Schiffer, Phys. Rev. 58, 064014 (1998)MathSciNetGoogle Scholar
  128. 128.
    C. Barceló, S. Liberati, M. Visser, Phys. Rev. A 68, 053613 (2003)ADSCrossRefGoogle Scholar
  129. 129.
    T.R. Slatyer, C.M. Savage, Class. Quant. Grav. 22, 3833 (2005)MATHMathSciNetADSCrossRefGoogle Scholar
  130. 130.
    S. Basak, P. Majumdar, Class. Quant. Grav. 20, 2929 (2000)MathSciNetADSCrossRefGoogle Scholar
  131. 131.
    S. Basak, P. Majumdar, Class. Quant. Grav. 20, 3907 (2000)MathSciNetADSCrossRefGoogle Scholar
  132. 132.
    F. Federici, C. Cherubini, S. Succi, M.P. Tosi, Phys. Rev. A 73, 033604 (2006)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • N. G. Parker
    • 1
  • B. Jackson
    • 2
  • A. M. Martin
    • 1
  • C. S. Adams
    • 3
  1. 1.University of MelbourneAustralia
  2. 2.Newcastle UniversityUK
  3. 3.Durham UniversityDurhamUk

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