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arXiv · 1401.2354

Stability of Bose-Einstein condensates in a $\mathcal{PT}$ symmetric double-$δ$ potential close to branch points

Andreas Löhle·Holger Cartarius·Daniel Haag·Dennis Dast·Jörg Main·Günter Wunner
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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 $\mathcal{PT}$ symmetric external potential. If the strength of the in- and outcoupling is increased two $\mathcal{PT}$ broken states bifurcate from the $\mathcal{PT}$ 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 $\mathcal{PT}$ symmetric double-$δ$ 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.

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Andreas Löhle, Holger Cartarius, Daniel Haag, Dennis Dast, Jörg Main, Günter Wunner. 2014-01-10. Stability of Bose-Einstein condensates in a $\mathcal{PT}$ symmetric double-$δ$ potential close to branch points. https://doi.org/10.14311/ap.2014.54.0133

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