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

Autor(en)

Michele Correggi, Nicolas Rougerie, Jakob Yngvason

Abstrakt

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1/epsilon (2) we consider the asymptotic regime epsilon -> 0 with the angular velocity Omega proportional to (epsilon (2)|log epsilon|)(-1). We prove that if Omega = Omega(0)(epsilon (2)|log epsilon|)(-1) and Omega(0) > 2(3 pi)(-1) 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.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Università degli Studi di Trento, Université de Cergy-Pontoise

Journal

Communications in Mathematical Physics

Band

303

Seiten

451-508

Anzahl der Seiten

58

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-011-1202-4

Publikationsdatum

2011

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/14f39bb8-3d3f-498e-ab80-369d5462cadd