Darmstadt 2008 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 37: Quantengase (Wechselwirkungseffekte I)

Q 37.8: Talk

Thursday, March 13, 2008, 12:45–13:00, 1C

Discovery of exceptional points in stationary states of Bose-Einstein condensates — •Holger Cartarius, Jörg Main, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart

The stationary Gross-Pitaevskii equation exhibits a nodeless solution which is born together with the ground state in a tangent bifurcation. The phenomenon has been demonstrated for condensat es in a harmonic trap and, recently, has also been found for condensates with attractive 1/r-interaction and condensates with dipole-dipole interaction. At the bifurcation point both states coalesce, i.e. the energies and the wave functions are identical, a situation known from exceptional points in linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions in the cases mentioned above show the same behavior as an exceptional point in a linear quantum system. For the self-trapping case of a condensate with 1/r-interaction we find analytic expressions directly demonstrating the branch point singularity structure of the states.