Q. Du
Qiang's Research Gallery 2  
  Quantized vortices in Bose-Einstein condensates and
  (find more details from Qiang's publications)


It is said that at temperatures close to absolute zero, something amazing happens: the state of superfluidity starts to appear. Superfluidity is a phase of matter characterised by the complete absence of viscosity, that is, a "fluid" can flow endlessly without friction (resistance).

Examples of superfluidity can be found in superconductors, Helium, and more recently in BEC gas. Quantized vortices are the signature of superfluidity.

When a bucket of water is placed on a rotating turn-table, gradually the water starts to rotate uniformly with the glass. Yet, the rotation of superfluid is inhomogeneous: it circulates around quantized vortex lines where the vorticity concentrate, and there is little vorticity outside of the lines.

Models to study the quantized vortices in BEC are often taken to be the Gross-Pitaevskii equations, which we have extensively studied and simulated.

There is a story of quantized vortices beyond rotation, as told in our PRL paper.

   BEC in symmetric trap, no rotation
BEC in symmetric trap, under rotation
Symmetric trap, different rotation frequency
Symmetric and nonsymmetric trap
BEC passing through cylinder (laser, details in PRL)
Illustration of BEC from MIT group
Names of some collaborators: A. Aftalion, W. Bao, Y. Pomeau

  1. Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime ,
    Phy Rev A, Dec 2001
       analyzing vortex state in BEC, similar to the G-L framework
       numerical computations of vortex solutions, 2d
  2. Dissipative Flow and Vortex Shedding in the Painleve Boundary Layer of a Bose-Einstein Condensate ,
    Phy Rev Lett., 91 (2003), 090407
       analyzing a recent MIT experiments with the laser probing of the BEC,
       explains the onset of dissipation and its relation to vortex shedding
  3. Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow,
    SIAM J. Sci. Comp., 25, pp. 1674-1697, 2004
  4. Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation,
    SIAM J. Scientific Comp., 66, pp. 758-786, 2006
  5. Diverse vortex dynamics in superfluids,
    Contemp Math. 329, pp105-117, AMS, 2003.
  6. More papers on the subject

Contact Qiang Du    2003-04-08