Stuttgart 2012 – wissenschaftliches Programm
Q 34.32: Poster
Dienstag, 13. März 2012, 16:30–19:00, Poster.I+II
Exceptional points at bifurcations in dipolar Bose-Einstein condensates — •Robin Gutöhrlein, Jörg Main, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart
The nonlinearity in the extended Gross-Pitaevskii equation (GPE) describing dipolar Bose-Einstein condensates (BECs) can lead to degeneracies of the wave functions. We obtain the stationary states of the GPE by applying the time-dependent variational principle using an ansatz of coupled Gaussians. For cylindrical traps the linear stability of the ground state changes at a critical value of the scattering length.
A detailed analysis shows that the stability change is related to a pitchfork bifurcation. This bifurcation point exhibits the signatures of an exceptional point. Breaking the symmetry of the external trap the exceptional point splits up into three different exceptional points located in the complex scattering length plane. Encircling various combinations of the three branch points reveals the permutation behavior of a square root (EP2) and a cubic root exceptional point (EP3).