The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

Michele Correggi (1) , Nicolas Rougerie (2) , Jakob Yngvason (3)

1 FBK - Fondazione Bruno Kessler [Trento, Italy]
2 LJLL - Laboratoire Jacques-Louis Lions
3 Erwin Schrödinger Institute for Mathematical Physics

Abstract: We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. We consider the strongly interacting regime where the coupling constant gets large. We prove that if the angular velocity is above some threshold fixed by the coupling constant then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary `hole' around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.

Mots clés: Bose-Einstein Condensates; Vortices; Giant Vortex.; Giant Vortex

Domaines: Analyse numérique [cs.NA]

Michele Correggi, Nicolas Rougerie, Jakob Yngvason. The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate. 2010. ⟨hal-00517386⟩