Hamburg 2009 – scientific programme

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A: Fachverband Atomphysik

A 5: Atomic Systems in External Fields I

A 5.1: Invited Talk

Monday, March 2, 2009, 16:30–17:00, VMP 6 HS-B

Exceptional points in atomic spectra and Bose-Einstein condensates — •Holger Cartarius, Jörg Main, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart

In parameter-dependent open quantum systems exceptional points can appear, at which both the complex energy eigenvalues and the wave functions describing two or even more resonances of the system pass through a branch point singularity as functions of the parameters, i.e. become identical. A real physical system which is accessible theoretically and experimentally and which exhibits exceptional points is the hydrogen atom in crossed external electric and magnetic fields. We show how exceptional points can be detected in numerical calculations, how they can be described with low-dimensional matrix models, and propose a method to verify their existence in an experiment with atoms. Important phenomena such as the geometric phase for closed loops around the critical parameter sets are demonstrated and the rare case of a connection between three resonances almost forming a triple-degeneracy in the form of a cubic root branch point is presented.

Furthermore, we extend the concept of exceptional points to the nonlinear Gross-Pitaevskii equation describing the stationary states of Bose-Einstein condensates. Here, they appear as bifurcation points at which two stationary states, a stable ground state and an unstable nodeless excited state, are born together in a tangent bifurcation.