Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps

Autor(en)

M Correggi, Tanja Rindler-Daller, Jakob Yngvason

Abstrakt

We study a rotating Bose-Einstein condensate in a strongly anharmonic

trap (flat trap with a finite radius) in the framework of

two-dimensional Gross-Pitaevskii theory. We write the coupling constant

for the interactions between the gas atoms as 1/ε2 and we are interested in the limit ε→0 (Thomas-Fermi limit) with the angular velocity Ω depending on ε. We derive rigorously the leading asymptotics of the ground state energy and the density profile when Ω tends to infinity as a power of 1∕ε. If Ω(ε)=Ω0∕ε a “hole” (i.e., a region where the density becomes exponentially small as 1∕ε→∞) develops for Ω0 above a certain critical value. If Ω(ε)⪢1/ε

the hole essentially exhausts the container and a “giant vortex”

develops with the density concentrated in a thin layer at the boundary.

While we do not analyze the detailed vortex structure we prove that

rotational symmetry is broken in the ground state for const∣logε∣<Ω(ε)≲const∕ε.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Erwin Schrödinger Institut

Journal

Journal of Mathematical Physics

Band

48

Anzahl der Seiten

30

ISSN

0022-2488

DOI

https://doi.org/10.1063/1.2712421

Publikationsdatum

2007

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/9005068b-3b17-4e71-b587-1742cf0d4c64