Stability of Bose-Einstein condensates in a $\mathcal{PT}$ symmetric double-$\delta$ potential close to branch points
Abstract
A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) with a symmetric external potential. If the strength of the in- and outcoupling is increased two broken states bifurcate from the symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a symmetric double- potential and calculate the stationary states. The ground state's stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.
Keywords
Cite
@article{arxiv.1401.2354,
title = {Stability of Bose-Einstein condensates in a $\mathcal{PT}$ symmetric double-$\delta$ potential close to branch points},
author = {Andreas Löhle and Holger Cartarius and Daniel Haag and Dennis Dast and Jörg Main and Günter Wunner},
journal= {arXiv preprint arXiv:1401.2354},
year = {2014}
}
Comments
6 pages, 4 figures