2008/09/10 by Nicolas Rougerie, Rougerie, Nicolas
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions
paper · pdf · doi:10.48550/arxiv.0809.1818
We study the fast rotation limit for a Bose-Einstein condensate in a quadratic plus quartic confining potential within the framework of the two dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to infinity with a proper scaling of the other parameters in the model, a linear limit problem appears for which we are able to derive precise energy estimates. We prove that the energy and density asymptotics of the problem can be obtained by minimizing a simplified one dimensional energy functional. In the case of a fixed coupling constant we also prove that a giant vortex state appears. It is an annulus with pure irrotational flow encircling a central low-density hole around which there is a macroscopic phase circulation.