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.
Similar content being viewed by others
References
A.J. Leggett, Superfluidity. Rev. Mod. Phys. 71(2), S318–S323 (1999)
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)
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)
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)
D. Guéry-Odelin, S. Stringari, Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas. Phys. Rev. Lett. 83(22), 4452–4455 (1999)
C. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, 2nd edn. (Cambridge University Press, Cambridge, 2008)
L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003)
A.L. Fetter, A.A. Svidzinsky, Vortices in a trapped dilute Bose-Einstein condensate. J. Phys., Condens. Matter 13(12), R135 (2001)
A.L. Fetter, Rotating trapped Bose-Einstein condensates. Rev. Mod. Phys. 81(2), 647–691 (2009)
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)
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)
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)
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)
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)
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)
S.R. Muniz, D.S. Naik, C. Raman, Bragg spectroscopy of vortex lattices in Bose-Einstein condensates. Phys. Rev. A 73(4), 041605 (2006)
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)
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)
M. Kobayashi, M. Tsubota, Quantum turbulence in a trapped Bose-Einstein condensate. Phys. Rev. A 76(4), 045603 (2007)
M. Tsubota, M. Kobayashi, Quantum turbulence in trapped atomic Bose-Einstein condensates. J. Low Temp. Phys. 150, 402 (2007)
W.F. Vinen, J.J. Niemela, Quantum turbulence. J. Low Temp. Phys. 128(5–6), 167–231 (2002)
M. Tsubota, Quantum turbulence - from superfluid helium to atomic BEC. J. Phys., Condens. Matter 21, 164207 (2009)
W.F. Vinen, Quantum turbulence: achievements and challenges. J. Low Temp. Phys. 161, 419 (2010)
M.S. Paoletti, D.P. Lathrop, Quantum turbulence. Ann. Rev. Condens. Matter Phys. 2, 213 (2011)
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)
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)
Y. Castin, R. Dum, Bose-Einstein condensates in time dependent traps. Phys. Rev. Lett. 71(3), 463–512 (1999)
F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 77(27), 5315 (1996)
A.L. Fetter, Vortices and dynamics in trapped Bose-Einstein condensates. J. Low Temp. Phys. 161, 445–459 (2010)
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)
S. Stringari, Collective excitations of a trapped Bose-condensed gas. Phys. Rev. Lett. 77, 2360–2363 (1996)
A. Sedrakian, I. Wasserman, Oscillations of rotating trapped Bose-Einstein condensates. Phys. Rev. A 63(6), 063605 (2001)
M. Cozzini, S. Stringari, Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice. Phys. Rev. A 67(4), 041602 (2003)
A.L. Fetter, Vortex nucleation in deformed rotating cylinders. J. Low Temp. Phys. 16(5/6), 533 (1974)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-011-0409-2