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Self-similar Expansion of the Density Profile in a Turbulent Bose-Einstein Condensate

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Abstract

In a recent study we demonstrated the emergence of turbulence in a trapped Bose-Einstein condensate of 87Rb atoms. An intriguing observation in such a system is the behavior of the turbulent cloud during free expansion. The aspect ratio of the cloud size does not change in the way one would expect for an ordinary non-rotating (vortex-free) condensate. Here we show that the anomalous expansion can be understood, at least qualitatively, in terms of the presence of vorticity distributed throughout the cloud, effectively counteracting the usual reversal of the aspect ratio seen in free time-of-flight expansion of non-rotating condensates.

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References

  1. A.J. Leggett, Superfluidity. Rev. Mod. Phys. 71(2), S318–S323 (1999)

    Article  MathSciNet  Google Scholar 

  2. O.M. Maragò, S.A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, C.J. Foot, Observation of the scissors mode and evidence for superfluidity of a trapped Bose-Einstein condensed gas. Phys. Rev. Lett. 84(10), 2056–2059 (2000)

    Article  ADS  Google Scholar 

  3. G. Hechenblaikner, E. Hodby, S.A. Hopkins, O.M. Maragò, C.J. Foot, Direct observation of irrotational flow and evidence of superfluidity in a rotating Bose-Einstein condensate. Phys. Rev. Lett. 88(7), 070406 (2002)

    Article  ADS  Google Scholar 

  4. M. Edwards, C.W. Clark, P. Pedri, L. Pitaevskii, S. Stringari, Consequence of superfluidity on the expansion of a rotating Bose-Einstein condensate. Phys. Rev. Lett. 88(7), 070405 (2002)

    Article  ADS  Google Scholar 

  5. D. Guéry-Odelin, S. Stringari, Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas. Phys. Rev. Lett. 83(22), 4452–4455 (1999)

    Article  ADS  Google Scholar 

  6. C. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, 2nd edn. (Cambridge University Press, Cambridge, 2008)

    Book  Google Scholar 

  7. L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003)

    MATH  Google Scholar 

  8. A.L. Fetter, A.A. Svidzinsky, Vortices in a trapped dilute Bose-Einstein condensate. J. Phys., Condens. Matter 13(12), R135 (2001)

    Article  ADS  Google Scholar 

  9. A.L. Fetter, Rotating trapped Bose-Einstein condensates. Rev. Mod. Phys. 81(2), 647–691 (2009)

    Article  ADS  Google Scholar 

  10. M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell, Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83(13), 2498–2501 (1999)

    Article  ADS  Google Scholar 

  11. K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Vortex formation in a stirred Bose-Einstein condensate. Phys. Rev. Lett. 84(5), 806–809 (2000)

    Article  ADS  Google Scholar 

  12. J.R. Abo-Shaeer, C. Raman, J.M. Vogels, W. Ketterle, Observation of vortex lattices in Bose-Einstein condensate. Science 292(5516), 476–479 (2001)

    Article  ADS  Google Scholar 

  13. K.W. Madison, F. Chevy, V. Bretin, J. Dalibard, Stationary states of a rotating Bose-Einstein condensate: Routes to vortex nucleation. Phys. Rev. Lett. 86(20), 4443–4446 (2001)

    Article  ADS  Google Scholar 

  14. Y. Shin, M. Saba, M. Vengalattore, T.A. Pasquini, C. Sanner, A.E. Leanhardt, M. Prentiss, D.E. Pritchard, W. Ketterle, Dynamical instability of a doubly quantized vortex in a Bose-Einstein condensate. Phys. Rev. Lett. 93(16), 160406 (2004)

    Article  ADS  Google Scholar 

  15. P. Engels, I. Coddington, P.C. Haljan, E.A. Cornell, Nonequilibrium effects of anisotropic compression applied to vortex lattices in Bose-Einstein condensates. Phys. Rev. Lett. 89(10), 100403 (2002)

    Article  ADS  Google Scholar 

  16. S.R. Muniz, D.S. Naik, C. Raman, Bragg spectroscopy of vortex lattices in Bose-Einstein condensates. Phys. Rev. A 73(4), 041605 (2006)

    Article  ADS  Google Scholar 

  17. E.A.L. Henn, J.A. Seman, E.R.F. Ramos, M. Caracanhas, P. Castilho, E.P. Olímpio, G. Roati, D.V. Magalhães, K.M.F. Magalhães, V.S. Bagnato, Observation of vortex formation in an oscillating trapped Bose-Einstein condensate. Phys. Rev. A 79(4), 043618 (2009)

    Article  ADS  Google Scholar 

  18. E.A.L. Henn, J.A. Seman, G. Roati, K.M.F. Magalhães, V.S. Bagnato, Emergence of turbulence in an oscillating Bose-Einstein condensate. Phys. Rev. Lett. 103(4), 045301 (2009)

    Article  ADS  Google Scholar 

  19. M. Kobayashi, M. Tsubota, Quantum turbulence in a trapped Bose-Einstein condensate. Phys. Rev. A 76(4), 045603 (2007)

    Article  ADS  Google Scholar 

  20. M. Tsubota, M. Kobayashi, Quantum turbulence in trapped atomic Bose-Einstein condensates. J. Low Temp. Phys. 150, 402 (2007)

    Article  ADS  Google Scholar 

  21. W.F. Vinen, J.J. Niemela, Quantum turbulence. J. Low Temp. Phys. 128(5–6), 167–231 (2002)

    Article  Google Scholar 

  22. M. Tsubota, Quantum turbulence - from superfluid helium to atomic BEC. J. Phys., Condens. Matter 21, 164207 (2009)

    Article  ADS  Google Scholar 

  23. W.F. Vinen, Quantum turbulence: achievements and challenges. J. Low Temp. Phys. 161, 419 (2010)

    Article  ADS  Google Scholar 

  24. M.S. Paoletti, D.P. Lathrop, Quantum turbulence. Ann. Rev. Condens. Matter Phys. 2, 213 (2011)

    Article  ADS  Google Scholar 

  25. E. Henn, J. Seman, G. Seco, E. Olimpio, P. Castilho, G. Roati, D. Magalhães, K. Magalhães, V. Bagnato, Bose-Einstein condensation in 87Rb-characterization of the Brazilian experiment. Braz. J. Phys., São Paulo 38, 279–286 (2008)

    Google Scholar 

  26. J.A. Seman, E.A.L. Henn, R.F. Shiozaki, G. Roati, F.J. Poveda-Cuevas, K.M.F. Magalhães, V.I. Yukalov, M. Tsubota, M. Kobayashi, K. Kasamatsu, V.S. Bagnato, Route to turbulence in a trapped Bose-Einstein condensate. Laser Phys. Lett. 8, 691–696 (2011)

    Google Scholar 

  27. Y. Castin, R. Dum, Bose-Einstein condensates in time dependent traps. Phys. Rev. Lett. 71(3), 463–512 (1999)

    Google Scholar 

  28. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 77(27), 5315 (1996)

    Google Scholar 

  29. A.L. Fetter, Vortices and dynamics in trapped Bose-Einstein condensates. J. Low Temp. Phys. 161, 445–459 (2010)

    Article  ADS  Google Scholar 

  30. D.S. Jin, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Collective excitations of a Bose-Einstein condensate in a dilute gas. Phys. Rev. Lett. 77, 420–423 (1996)

    Article  ADS  Google Scholar 

  31. S. Stringari, Collective excitations of a trapped Bose-condensed gas. Phys. Rev. Lett. 77, 2360–2363 (1996)

    Article  ADS  Google Scholar 

  32. A. Sedrakian, I. Wasserman, Oscillations of rotating trapped Bose-Einstein condensates. Phys. Rev. A 63(6), 063605 (2001)

    Article  ADS  Google Scholar 

  33. M. Cozzini, S. Stringari, Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice. Phys. Rev. A 67(4), 041602 (2003)

    Article  ADS  Google Scholar 

  34. A.L. Fetter, Vortex nucleation in deformed rotating cylinders. J. Low Temp. Phys. 16(5/6), 533 (1974)

    Article  ADS  Google Scholar 

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Correspondence to S. R. Muniz.

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Caracanhas, M., Fetter, A.L., Muniz, S.R. et al. Self-similar Expansion of the Density Profile in a Turbulent Bose-Einstein Condensate. J Low Temp Phys 166, 49–58 (2012). https://doi.org/10.1007/s10909-011-0409-2

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  • DOI: https://doi.org/10.1007/s10909-011-0409-2

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