Skip to main content
SpringerLink
Log in

Impact of Density Inhomogeneity on the Critical Velocity for Vortex Shedding in a Harmonically Trapped Bose–Einstein Condensate

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

We report on a numerical study of the critical velocity for creation of quantized vortices by a moving Gaussian obstacle in a trapped Bose–Einstein condensate, modeled by the Gross–Pitaevskii equation. We pay attention to impact of density inhomogeneity associated with the global inverted parabolic profile by a trapping potential as well as the local density suppression around the Gaussian obstacle. When the width of the Gaussian potential is large, the wake dynamics is significantly influenced by the nonuniformity around the obstacle potential. The critical velocity, estimated through the time interval between the first and second vortex emission, can be explained by the local sound velocity by taking into account the above two contributions. We find that the ratio of the critical velocity for vortex creation to the sound velocity at the center of the system is minimally influenced by the nonlinear coefficient in the Gross–Pitaevskii equation. This result implies that the analysis in the homogeneous system is directly applicable to the inhomogeneous trapped condensates under the local density approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. L. Landau, Theory of the superfluidity of helium II. Phys. Rev. 60(4), 356–358 (1941)

    Article  ADS  CAS  Google Scholar 

  2. C. Raman, M. Köhl, R. Onofrio, D.S. Durfee, C.E. Kuklewicz, Z. Hadzibabic, W. Ketterle, Evidence for a critical velocity in a Bose–Einstein condensed gas. Phys. Rev. Lett. 83(13), 2502–2505 (1999)

    Article  ADS  CAS  Google Scholar 

  3. R. Onofrio, C. Raman, J.M. Vogels, J.R. Abo-Shaeer, A.P. Chikkatur, W. Ketterle, Observation of superfluid flow in a Bose–Einstein condensed gas. Phys. Rev. Lett. 85(11), 2228–2231 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  4. W.J. Kwon, G. Moon, S.W. Seo, Y. Shin, Critical velocity for vortex shedding in a Bose–Einstein condensate. Phys. Rev. A 91(5), 053615 (2015)

    Article  ADS  Google Scholar 

  5. W.J. Kwon, J.H. Kim, S.W. Seo, Y. Shin, Observation of von kármán vortex street in an atomic superfluid gas. Phys. Rev. Lett. 117(24), 245301 (2016)

    Article  ADS  PubMed  Google Scholar 

  6. Y. Lim, Y. Lee, J. Goo, D. Bae, Y. Shin, Vortex shedding frequency of a moving obstacle in a Bose–Einstein condensate. New J. Phys. 24(8), 083020 (2022)

    Article  ADS  Google Scholar 

  7. W.J. Kwon, G. Del Pace, K. Xhani, L. Galantucci, A. Muzi Falconi, M. Inguscio, F. Scazza, G. Roati, Sound emission and annihilations in a programmable quantum vortex collider. Nature 600(7887), 64–69 (2021)

    Article  ADS  CAS  PubMed  Google Scholar 

  8. J.W. Park, B. Ko, Y. Shin, Critical vortex shedding in a strongly interacting fermionic superfluid. Phys. Rev. Lett. 121(22), 225301 (2018)

    Article  ADS  CAS  PubMed  Google Scholar 

  9. W. Weimer, K. Morgener, V.P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, H. Moritz, Critical velocity in the BEC-BCS crossover. Phys. Rev. Lett. 114(9), 095301 (2015)

    Article  ADS  PubMed  Google Scholar 

  10. A. Amo, J. Lefrére, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, A. Bramati, Superfluidity of polaritons in semiconductor microcavities. Nat. Phys. 5(11), 805–810 (2009)

    Article  CAS  Google Scholar 

  11. A. Amo, S. Pigeon, D. Sanvitto, V.G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, A. Bramati, Polariton superfluids reveal quantum hydrodynamic solitons. Science 332(6034), 1167–1170 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  12. G. Nardin, G. Grosso, Y. Léger, B. Piȩtka, F. Morier-Genoud, B. Deveaud-Plédran, Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid. Nat. Phys. 7(8), 635–641 (2011)

    Article  CAS  Google Scholar 

  13. G. Lerario, A. Fieramosca, F. Barachati, D. Ballarini, K.S. Daskalakis, L. Dominici, M. De Giorgi, S.A. Maier, G. Gigli, S. Kéna-Cohen, D. Sanvitto, Room-temperature superfluidity in a polariton condensate. Nat. Phys. 13(9), 837–841 (2017)

    Article  CAS  Google Scholar 

  14. T. Frisch, Y. Pomeau, S. Rica, Transition to dissipation in a model of superflow. Phys. Rev. Lett. 69(11), 1644–1647 (1992)

    Article  ADS  CAS  PubMed  Google Scholar 

  15. C. Nore, C. Huepe, M.E. Brachet, Subcritical dissipation in three-dimensional superflows. Phys. Rev. Lett. 84(10), 2191–2194 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  16. A. Aftalion, Q. Du, Y. Pomeau, Dissipative flow and vortex shedding in the Painlevé boundary layer of a Bose–Einstein condensate. Phys. Rev. Lett. 91(9), 090407 (2003)

    Article  ADS  PubMed  Google Scholar 

  17. M.T. Reeves, T.P. Billam, B.P. Anderson, A.S. Bradley, Identifying a superfluid Reynolds number via dynamical similarity. Phys. Rev. Lett. 114(15), 155302 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  18. H. Kwak, J.H. Jung, Y. Shin, Minimum critical velocity of a gaussian obstacle in a Bose–Einstein condensate. Phys. Rev. A 107(2), 023310 (2023)

    Article  ADS  CAS  Google Scholar 

  19. G.W. Stagg, N.G. Parker, C.F. Barenghi, Quantum analogues of classical wakes in Bose–Einstein condensates. J. Phys. B: At. Mol. Opt. Phys. 47(9), 095304 (2014)

    Article  ADS  Google Scholar 

  20. B. Jackson, J.F. McCann, C.S. Adams, Vortex formation in dilute inhomogeneous Bose–Einstein condensates. Phys. Rev. Lett. 80(18), 3903–3906 (1998)

    Article  ADS  CAS  Google Scholar 

  21. T. Winiecki, B. Jackson, J.F. McCann, C.S. Adams, Vortex shedding and drag in dilute Bose–Einstein condensates. J. Phys. B: At. Mol. Opt. Phys. 33(19), 4069–4078 (2000)

    Article  ADS  CAS  Google Scholar 

  22. S. Musser, D. Proment, M. Onorato, W.T.M. Irvine, Starting flow past an airfoil and its acquired lift in a superfluid. Phys. Rev. Lett. 123(15), 154502 (2019)

    Article  ADS  CAS  PubMed  Google Scholar 

  23. H. Kiehn, V.P. Singh, L. Mathey, Superfluidity of a laser-stirred Bose–Einstein condensate. Phys. Rev. A 105(4), 043317 (2022)

    Article  ADS  CAS  Google Scholar 

  24. M. Kunimi, Y. Kato, Metastability, excitations, fluctuations, and multiple-swallowtail structures of a superfluid in a Bose–Einstein condensate in the presence of a uniformly moving defect. Phys. Rev. A 91(5), 053608 (2015)

    Article  ADS  Google Scholar 

  25. F. Pinsker, N.G. Berloff, Transitions and excitations in a superfluid stream passing small impurities. Phys. Rev. A 89(5), 053605 (2014)

    Article  ADS  Google Scholar 

  26. K. Sasaki, N. Suzuki, H. Saito, Bènard–von Kàrmàn Vortex street in a Bose–Einstein condensate. Phys. Rev. Lett. 104(15), 150404 (2010)

    Article  ADS  PubMed  Google Scholar 

  27. S. Rica, A remark on the critical speed for vortex nucleation in the nonlinear Schrödinger equation. Physica D 148(3), 221–226 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  28. C.-T. Pham, C. Nore, M.É. Brachet, Boundary layers and emitted excitations in nonlinear Schrödinger superflow past a disk. Physica D 210(3), 203–226 (2005)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. G. Baym, C.J. Pethick, Ground-state properties of magnetically trapped Bose-condensed rubidium gas. Phys. Rev. Lett. 76(1), 6–9 (1996)

    Article  ADS  CAS  PubMed  Google Scholar 

  30. T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, B.P. Anderson, Observation of vortex dipoles in an oblate Bose–Einstein condensate. Phys. Rev. Lett. 104(16), 160401 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  31. W.J. Kwon, S.W. Seo, Y. Shin, Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose–Einstein condensate. Phys. Rev. A 92(3), 033613 (2015)

    Article  ADS  Google Scholar 

  32. C. Huepe, M.-E. Brachet, Scaling laws for vortical nucleation solutions in a model of superflow. Physica D 140(1), 126–140 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  33. F. Piazza, L.A. Collins, A. Smerzi, Instability and vortex ring dynamics in a three-dimensional superfluid flow through a constriction. New J. Phys. 13(4), 043008 (2011)

    Article  ADS  Google Scholar 

  34. F. Piazza, L.A. Collins, A. Smerzi, Critical velocity for a toroidal Bose–Einstein condensate flowing through a barrier. J. Phys. B: At. Mol. Opt. Phys. 46(9), 095302 (2013)

    Article  ADS  CAS  Google Scholar 

  35. J.S. Stießberger, W. Zwerger, Critcal velocity of superfluid flow past large obstacles in Bose–Einstein condensates. Phys. Rev. A 62(6), 061601 (2000)

    Article  ADS  Google Scholar 

Download references

Author information

Author notes

  1. Haruya Kokubo and Kenichi Kasamatsu have contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Kindai University, 3-4-1 Kowakae, Higashi Osaka-city, Osaka, 577-8502, Japan

    Haruya Kokubo & Kenichi Kasamatsu

Authors
  1. Haruya Kokubo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kenichi Kasamatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haruya Kokubo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kokubo, H., Kasamatsu, K. Impact of Density Inhomogeneity on the Critical Velocity for Vortex Shedding in a Harmonically Trapped Bose–Einstein Condensate. J Low Temp Phys 214, 427–441 (2024). https://doi.org/10.1007/s10909-024-03054-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-024-03054-9

Keywords

Search

Navigation