Hannover 2016 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 63: Ultra-cold atoms, ions and BEC V (with A)

Q 63.3: Talk

Friday, March 4, 2016, 11:30–11:45, f107

Topological Bogoliubov excitations of weakly interacting Bose-Einstein condensates — •Georg Engelhardt and Tobias Brandes — Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin

Topological band structures have been mostly investigated for fermionic systems. In our talk, we explain how to generalize the notion of topology to Bogoliubov excitations on top of a Bose-Einstein condensate. We investigate the topology of these Bogoliubov excitations in inversion-invariant systems of weakly interacting bosons.

The excitations of the corresponding Bogoliubov Hamiltonian have to be diagonalized in a symplectic manner. Analogously to the fermionic case, we here establish a symplectic extension of the polarization characterizing the topology of the Bogoliubov excitations and link it to the eigenvalues of the inversion operator at the inversion-invariant momenta.

We show that the interaction of the particles influences the topology of the Bogoliubov excitations. Additionally, we demonstrate that this quantity is related to edge states in the excitation spectrum of a finite-size system with boundaries.