Resonances and Dynamical Fragmentation in a Stirred Bose–Einstein Condensate

Abstract

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2

Notes

  1. 1.

    For a choice of \(L=30\,{\upmu }\)m, the parameter \(\sigma \) corresponds to \(300\,{\upmu }\)nm and the maximal extent of the cloud is \(180\,{\upmu }\)m. If, for instance, \(\omega _z=225\mathrm{Hz}\) and \(\omega _r=0.812\,\mathrm{Hz}\) are the values of the transverse and radial confinement frequencies, respectively, then the corresponding scattering length of our simulations would be \(\alpha _s \approx ~24\,\mathrm{nm}\approx ~50 \alpha _0\) (Bohr radii) and the interaction parameter \(g_0=0.5\).

  2. 2.

    We mean here local density bumps that resemble bright solitons; however, they are not real solitons as they do not propagate in time without dispersion.

References

  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)

    Article  ADS  Google Scholar 

  3. 3.

    T. Winiecki, J.F. McCann, C.S. Adams, Phys. Rev. Lett. 82, 5186 (1999)

    Article  ADS  Google Scholar 

  4. 4.

    B.M. Caradoc-Davies, R.J. Ballagh, K. Burnett, Phys. Rev. Lett. 83, 891 (1999)

    Article  ADS  Google Scholar 

  5. 5.

    K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Phys. Rev. Lett. 84, 806 (2000)

    Article  ADS  Google Scholar 

  6. 6.

    K.W. Madison, F. Chevy, V. Bretin, J. Dalibard, Phys. Rev. Lett. 86, 4443 (2001)

    Article  ADS  Google 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)

  8. 8.

    C. Raman, J.R. Abo-Shaeer, J.M. Vogels, K. Xu, W. Ketterle, Phys. Rev. Lett. 87, 210402 (2001)

    Article  ADS  Google Scholar 

  9. 9.

    T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, B.P. Anderson, Phys. Rev. Lett. 104, 160401 (2010)

    Article  ADS  Google Scholar 

  10. 10.

    E.G. Khamis, A. Gammal, Phys. Rev. A 87, 045601 (2013)

    Article  ADS  Google Scholar 

  11. 11.

    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. Lett. 80, 3903 (1998)

    Article  ADS  Google Scholar 

  12. 12.

    M. Tsubota, K. Kasamatsu, M. Ueda, J. Low Temp. Phys. 126, 461 (2002)

    Article  ADS  Google Scholar 

  13. 13.

    E. Lundh, J.P. Martikainen, K.A. Suominen, Phys. Rev. A 67, 063604 (2003)

    Article  ADS  Google Scholar 

  14. 14.

    D. Dagnino, N. Barberán, M. Lewenstein, J. Dalibard, Nat. Phys. 5, 431 (2009)

    Article  Google Scholar 

  15. 15.

    N.K. Wilkin, J.M.F. Gunn, R.A. Smith, Phys. Rev. Lett. 80, 2265 (1998)

    Article  ADS  Google Scholar 

  16. 16.

    E.J. Mueller, T.-L. Ho, M. Ueda, G. Baym, Phys. Rev. A 74, 033612 (2006)

    Article  ADS  Google Scholar 

  17. 17.

    B. Chakrabarti, T.K. Das, P.K. Debnath, J. Low Temp. Phys. 157, 527 (2009)

    Article  ADS  Google Scholar 

  18. 18.

    M.C. Tsatsos, Phys. Rev. A 89, 043604 (2014)

    Article  ADS  Google Scholar 

  19. 19.

    M.C. Tsatsos, A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. A 82, 033613 (2010)

    Article  ADS  Google Scholar 

  20. 20.

    O.I. Streltsova, O.E. Alon, L.S. Cederbaum, A.I. Streltsov, Phys. Rev. A 89, 061602(R) (2014)

    Article  ADS  Google Scholar 

  21. 21.

    U.R. Fischer, P. Bader, Phys. Rev. A 82, 013607 (2010)

    Article  ADS  Google 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)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

  25. 25.

    O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 77, 033613 (2008)

    Article  ADS  Google Scholar 

  26. 26.

    E.A. Cornell, personal communication

  27. 27.

    C.N. Friedman, J. Funct. Anal. 10, 346 (1972)

    MATH  Article  Google Scholar 

  28. 28.

    R.A. Doganov, S. Klaiman, O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 87, 033631 (2013)

    Article  ADS  Google Scholar 

  29. 29.

    A.U.J. Lode and M.C. Tsatsos, The recursive multiconfigurational time-dependent Hartree for Bosons Package, version 1.0, (2014), http://ultracold.org. 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)

    Article  ADS  Google Scholar 

  31. 31.

    Lode A.U.J. Tunneling Dynamics in Open Ultracold Bosonic Systems, Springer Theses, Springer Heidelberg, (2014)

  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)

    Article  ADS  Google Scholar 

  33. 33.

    G. Zürn, A.N. Wenz, S. Murmann, A. Bergschneider, T. Lompe, S. Jochim, Phys. Rev. Lett. 111, 175302 (2013)

    Article  ADS  Google Scholar 

  34. 34.

    C.F. Ockeloen, A.F. Tauschinsky, R.J.C. Spreeuw, S. Whitlock, Phys. Rev. A 82, 061606 (2010)

    Article  ADS  Google Scholar 

  35. 35.

    A.J. Coleman, V.I. Yukalov, Reduced Density Matrices: Coulsons Challenge (Springer, Berlin, 2000)

    Google 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)

    Article  ADS  Google Scholar 

  38. 38.

    V.I. Yukalov, A.N. Novikov, V.S. Bagnato, Laser Phys. Lett. 11, 095501 (2014)

    Article  ADS  Google 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)

    Article  ADS  Google Scholar 

  40. 40.

    A.J. Allen, N.G. Parker, N.P. Proukakis, C.F. Barenghii, Phys. Rev. A 89, 025602 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. C. Tsatsos.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tsatsos, M.C., Lode, A.U.J. Resonances and Dynamical Fragmentation in a Stirred Bose–Einstein Condensate. J Low Temp Phys 181, 171–181 (2015). https://doi.org/10.1007/s10909-015-1335-5

Download citation

Keywords

  • Ultracold Bose gas
  • Quantized vortex
  • Phantom vortex
  • Many-body physics
  • MCTDHB
  • http://ultracold.org