The European Physical Journal Special Topics

, Volume 147, Issue 1, pp 133–152 | Cite as

Vortex rings and solitary waves in trapped Bose–Einstein condensates

  • S. Komineas
Article

Abstract.

We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion of these solitary waves exhibits characteristics similar to a mode proposed sometime ago by Lieb in a strictly 1D model, as well as some rotonlike features. We subsequently discuss interactions between solitary waves. Head-on collisions between dark solitons are elastic. Slow vortex rings collide elastically but faster ones form intermediate structures during collisions before they lose energy to the background fluid. Solitary waves and their interactions have been observed in experiments. However, some of their intriguing features still remain to be experimentally identified.

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References

  1. E.A. Cornell, C.E. Wieman, Rev. Mod. Phys. 74, 875 (2002) Google Scholar
  2. W. Ketterle, Rev. Mod. Phys. 74, 1131 (2002) Google Scholar
  3. C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995) Google Scholar
  4. V. Bretin, S. Stock, Y. Seurin, J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004) Google Scholar
  5. L. Lesanovsky, W. von Klitzing, cond-mat/0612213 Google Scholar
  6. E.H. Lieb, W. Liniger, Phys. Rev. 130, 1605 (1964) Google Scholar
  7. E.H. Lieb, Phys. Rev. 130, 1616 (1964) Google Scholar
  8. T. Tsuzuki, J. Low Temp. Phys. 4, 441 (1973) Google Scholar
  9. V.E. Zakharov, A.B. Sabat, Sov. Phys. JETP 37, 823 (1973) Google Scholar
  10. P.P. Kulish, S.V. Manakov, L.D. Faddeev, Theor. Math. Phys. 28, 615 (1976) Google Scholar
  11. M. Ishikawa, H. Takayama, J. Phys. Soc. Jpn. 49, 1242 (1980) Google Scholar
  12. S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G.V. Shlyapnikov, M. Lewenstein, Phys. Rev. Lett. 83, 5198 (1999) Google Scholar
  13. J. Denschlag, J.E. Simsarian, D.L. Feder, C.W. Clark, L.A. Collins, J. Gubizolles, L. Deng, E.W. Hagley, K. Helmerson, W.P. Reinhardt, S.L. Rolston, B.I. Schneider, W.D. Phillips, Science 287, 97 (2000) Google Scholar
  14. 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) Google Scholar
  15. Z. Dutton, M. Budde, C. Slowe, L.V. Hau, Science 293, 663 (2001) Google Scholar
  16. N.S. Ginsberg, J. Brand, L.V. Hau, Phys. Rev. Lett. 94, 040403 (2005) Google Scholar
  17. E.P. Gross, Nuovo Cimento 20, 454 (1961) Google Scholar
  18. E.P. Gross, J. Math. Phys. 4, 195 (1963) Google Scholar
  19. L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961) Google Scholar
  20. S. Komineas, N. Papanicolaou, Phys. Rev. Lett. 89, 070402 (2002) Google Scholar
  21. S. Komineas, N. Papanicolaou, Phys. Rev. A 67, 023615 (2003) Google Scholar
  22. G. Baym, C.J. Pethick, Phys. Rev. Lett. 76, 6 (1996) Google Scholar
  23. V.M. Perez-Garcia, H. Michinel, H. Herrero, Phys. Rev. A 57, 3837 (1998) Google Scholar
  24. W.P. Reinhardt, C.W. Clark, J. Phys. B 30, L785 (1997) Google Scholar
  25. A.D. Jackson, G.M. Kavoulakis, C.J. Pethick, Phys. Rev. A 58, 2417 (1998) Google Scholar
  26. A.E. Muryshev, H.B. van Linden van den Heuvell, G.V. Shlyapnikov, Phys. Rev. A 60, R2665 (1999) Google Scholar
  27. T. Busch, J.R. Anglin, Phys. Rev. Lett. 84, 2298 (2000) Google Scholar
  28. D.L. Feder, M.S. Pindzola, L.A. Collins, B.I. Schneider, C.W. Clark, Phys. Rev. A 62, 053606 (2000) Google Scholar
  29. L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 65, 043614 (2002) Google Scholar
  30. N.G. Parker, N.P. Proukakis, M. Leadbeater, C.S. Adams, Phys. Rev. Lett. 90, 220401 (2003) Google Scholar
  31. G. Theocharis, P. Schmelcher, M.K. Oberthaler, P.G. Kevrekidis, D.J. Fratzeskakis, Phys. Rev. A 72, 023609 (2005) Google Scholar
  32. I.V. Barashenkov, E.Y. Panova, Physica D 69, 114 (1993) Google Scholar
  33. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967) Google Scholar
  34. P.G. Saffman, Vortex Dynamics (Cambridge University Press, Cambridge, 1992) Google Scholar
  35. C.A. Jones, P.H. Roberts, J. Phys. A: Math. Gen. 15, 2599 (1982) Google Scholar
  36. S. Komineas, N. Papanicolaou, Phys. Rev. A 68, 043617 (2003) Google Scholar
  37. A.D. Jackson, G.M. Kavoulakis, Phys. Rev. Lett. 89, 070403 (2002) Google Scholar
  38. S. Komineas, N. Papanicolaou, Laser Phys. 14, 571 (2004) Google Scholar
  39. R. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991) Google Scholar
  40. L. Carr, C.W. Clark, Phys. Rev. A 74, 043613 (2006) Google Scholar
  41. M. Leadbeater, D.C. Samuels, C.F. Barenghi, C.S. Adams, Phys. Rev. Lett. 86, 1410 (2001) Google Scholar
  42. J. Ruostekoski, Z. Dutton, Phys. Rev. A 72, 063626 (2005) Google Scholar
  43. C.F. Barenghi, R.J. Donnelly, W.F. Vinen, Quantized Vortex Dynamics and Superfluid Turbulence (Springer-Verlag, Berlin, Heidelberg, 2001) Google Scholar
  44. M.J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (SIAM, 1981) Google Scholar
  45. J. Koplik, H. Levine, Phys. Rev. Lett. 76, 4745 (1996) Google Scholar
  46. N. Berloff, J. Phys. A 37, 1617 (2004) Google Scholar
  47. S. Komineas, J. Brand, Phys. Rev. Lett. 95, 110401 (2005) Google Scholar
  48. L.K.S.W. Thomson, Nature 24, 47 (1881) Google Scholar
  49. L.D. Carr, J. Brand, Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment, edited by P.G. Kevrekidis, D.J. Frantzeskakis, R. Carretero (Springer, Heidelberg, 2007), Ch. Va Google Scholar
  50. J. Brand, W.P. Reinhardt, J. Phys. B: At. Mol. Opt. Phys. 34, L113 (2001) Google Scholar
  51. J. Brand, W.P. Reinhardt, Phys. Rev. A 65, 043612 (2002) Google Scholar
  52. J. Brand, L.D. Carr, B.P. Anderson, Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment, edited by P.G. Kevrekidis, D.J. Frantzeskakis, R. Carretero (Springer, Heidelberg, 2007), Ch. Vb Google Scholar
  53. E.R. Huggins, Phys. Rev. Lett. 29, 1067 (1972) Google Scholar
  54. A.L. Fetter, Phys. Rev. A 6, 402 (1972) Google Scholar
  55. M.C. Cross, Phys. Rev. A 10, 1442 (1974) Google Scholar
  56. G. Gamota, M. Barmatz, Phys. Rev. Lett. 22, 874 (1969) Google Scholar
  57. Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • S. Komineas
    • 1
  1. 1.Max-Planck-Institute for the Physics of Complex SystemsDresdenGermany

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