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

Andreas Löhle, Holger Cartarius, Daniel Haag, Dennis Dast, Jörg Main, Günter Wunner

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-$$\delta$$ 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.

http://arxiv.org/abs/1401.2354
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Chaotic Dynamics (nlin.CD)