Journal of Low Temperature Physics

, Volume 181, Issue 3–4, pp 171–181 | Cite as

Resonances and Dynamical Fragmentation in a Stirred Bose–Einstein Condensate

  • M. C. TsatsosEmail author
  • A. U. J. Lode


Superfluids are distinguished from ordinary fluids by the quantized manner in which the rotation is manifested in them. Precisely, quantized vortices are known to appear in the bulk of a superfluid subject to external rotation. In this work we study a trapped ultracold Bose gas of \(N=101\) atoms interacting with finite-range potential in two spatial dimensions that is stirred by a rotating beam. We use the multiconfigurational Hartree method for bosons, which goes beyond the mainstream mean-field theory, to calculate the dynamics of the gas in real time. As the gas is rotated, the wavefunction of the system changes symmetry and topology. We see a series of resonances, i.e., peaks in the total energy, as the stirring frequency is increased. Fragmentation and a change of the symmetry of the density of the gas accompany the appearance of these resonances. We conclude that fragmentation of the gas appears hand-in-hand with resonant absorption of energy and angular momentum from the external agent of rotation.


Ultracold Bose gas Quantized vortex Phantom vortex Many-body physics MCTDHB 



We thank V.S. Bagnato and S. Weiner for essential and useful comments on the manuscript. M.C.T acknowledges financial support from FAPESP. A.U.J.L. acknowledges financial support by the Swiss SNF and the NCCR Quantum Science and Technology. Computational time in the Hermit Cray computer of the HLRS is also gratefully acknowledged. Last, A.U.J.L. thanks Centro de Pesquisas em Óptica e Fotônica (CEPOF) of the Institute of Physics of São Carlos (IFSC) of the University of São Paulo (USP) for generous hospitality.


  1. 1.
    C. Pethick, H. Smith, Bose–Einstein Condensations in Dilute Gases (Cambridge University Press, Cambridge, 2002)Google Scholar
  2. 2.
    D. Butts, D. Rokhsar, Nature 397, 327 (1999)CrossRefADSGoogle Scholar
  3. 3.
    T. Winiecki, J.F. McCann, C.S. Adams, Phys. Rev. Lett. 82, 5186 (1999)CrossRefADSGoogle Scholar
  4. 4.
    B.M. Caradoc-Davies, R.J. Ballagh, K. Burnett, Phys. Rev. Lett. 83, 891 (1999)CrossRefADSGoogle Scholar
  5. 5.
    K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Phys. Rev. Lett. 84, 806 (2000)CrossRefADSGoogle Scholar
  6. 6.
    K.W. Madison, F. Chevy, V. Bretin, J. Dalibard, Phys. Rev. Lett. 86, 4443 (2001)CrossRefADSGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    C. Raman, J.R. Abo-Shaeer, J.M. Vogels, K. Xu, W. Ketterle, Phys. Rev. Lett. 87, 210402 (2001)CrossRefADSGoogle Scholar
  9. 9.
    T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, B.P. Anderson, Phys. Rev. Lett. 104, 160401 (2010)CrossRefADSGoogle Scholar
  10. 10.
    E.G. Khamis, A. Gammal, Phys. Rev. A 87, 045601 (2013)CrossRefADSGoogle Scholar
  11. 11.
    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. Lett. 80, 3903 (1998)CrossRefADSGoogle Scholar
  12. 12.
    M. Tsubota, K. Kasamatsu, M. Ueda, J. Low Temp. Phys. 126, 461 (2002)CrossRefADSGoogle Scholar
  13. 13.
    E. Lundh, J.P. Martikainen, K.A. Suominen, Phys. Rev. A 67, 063604 (2003)CrossRefADSGoogle Scholar
  14. 14.
    D. Dagnino, N. Barberán, M. Lewenstein, J. Dalibard, Nat. Phys. 5, 431 (2009)CrossRefGoogle Scholar
  15. 15.
    N.K. Wilkin, J.M.F. Gunn, R.A. Smith, Phys. Rev. Lett. 80, 2265 (1998)CrossRefADSGoogle Scholar
  16. 16.
    E.J. Mueller, T.-L. Ho, M. Ueda, G. Baym, Phys. Rev. A 74, 033612 (2006)CrossRefADSGoogle Scholar
  17. 17.
    B. Chakrabarti, T.K. Das, P.K. Debnath, J. Low Temp. Phys. 157, 527 (2009)CrossRefADSGoogle Scholar
  18. 18.
    M.C. Tsatsos, Phys. Rev. A 89, 043604 (2014)CrossRefADSGoogle Scholar
  19. 19.
    M.C. Tsatsos, A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. A 82, 033613 (2010)CrossRefADSGoogle Scholar
  20. 20.
    O.I. Streltsova, O.E. Alon, L.S. Cederbaum, A.I. Streltsov, Phys. Rev. A 89, 061602(R) (2014)CrossRefADSGoogle Scholar
  21. 21.
    U.R. Fischer, P. Bader, Phys. Rev. A 82, 013607 (2010)CrossRefADSGoogle Scholar
  22. 22.
    J.C. Cremon, A.D. Jackson, E.O. Karabulut, G.M. Kavoulakis, B.R. Mottelson, S.M. Reimann, Phys. Rev. A 91, 033623 (2015)CrossRefADSGoogle Scholar
  23. 23.
    S.E. Weiner, M.C. Tsatsos, L.S. Cederbaum, and A.U.J. Lode, arXiv:1409.7670
  24. 24.
    A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. Lett. 99, 030402 (2007)CrossRefADSGoogle Scholar
  25. 25.
    O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 77, 033613 (2008)CrossRefADSGoogle Scholar
  26. 26.
    E.A. Cornell, personal communicationGoogle Scholar
  27. 27.
    C.N. Friedman, J. Funct. Anal. 10, 346 (1972)zbMATHCrossRefGoogle Scholar
  28. 28.
    R.A. Doganov, S. Klaiman, O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 87, 033631 (2013)CrossRefADSGoogle Scholar
  29. 29.
    A.U.J. Lode and M.C. Tsatsos, The recursive multiconfigurational time-dependent Hartree for Bosons Package, version 1.0, (2014), Accessed 07 Sept 2015
  30. 30.
    A.U.J. Lode, K. Sakmann, O.E. Alon, L.S. Cederbaum, A.I. Streltsov, Phys. Rev. A 86, 063606 (2012)CrossRefADSGoogle Scholar
  31. 31.
    Lode A.U.J. Tunneling Dynamics in Open Ultracold Bosonic Systems, Springer Theses, Springer Heidelberg, (2014)Google Scholar
  32. 32.
    I. Březinová, A.U.J. Lode, A.I. Streltsov, O.E. Alon, L.S. Cederbaum, J. Burgdörfer, Phys. Rev. A 86, 013630 (2012)CrossRefADSGoogle Scholar
  33. 33.
    G. Zürn, A.N. Wenz, S. Murmann, A. Bergschneider, T. Lompe, S. Jochim, Phys. Rev. Lett. 111, 175302 (2013)CrossRefADSGoogle Scholar
  34. 34.
    C.F. Ockeloen, A.F. Tauschinsky, R.J.C. Spreeuw, S. Whitlock, Phys. Rev. A 82, 061606 (2010)CrossRefADSGoogle Scholar
  35. 35.
    A.J. Coleman, V.I. Yukalov, Reduced Density Matrices: Coulsons Challenge (Springer, Berlin, 2000)CrossRefGoogle Scholar
  36. 36.
    A.U.J. Lode, B. Chakrabarti, V.K.B. Kota, arXiv:1501.02611 [cond-mat.quant-gas] (2015)
  37. 37.
    S. Sinha, Y. Castin, Phys. Rev. Lett. 87, 190402 (2001)CrossRefADSGoogle Scholar
  38. 38.
    V.I. Yukalov, A.N. Novikov, V.S. Bagnato, Laser Phys. Lett. 11, 095501 (2014)CrossRefADSGoogle Scholar
  39. 39.
    J. Grond, A.I. Streltsov, A.U.J. Lode, K. Sakmann, L.S. Cederbaum, O.E. Alon, Phys. Rev. A 88, 023606 (2013)CrossRefADSGoogle Scholar
  40. 40.
    A.J. Allen, N.G. Parker, N.P. Proukakis, C.F. Barenghii, Phys. Rev. A 89, 025602 (2012)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Instituto de Física de São CarlosUniversidade de São PauloSão CarlosBrazil
  2. 2.Department of PhysicsUniversity of BaselBaselSwitzerland

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