# Berlin 2014 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 32: Poster: Quantum gases, ultracold atoms and molecules

### Q 32.53: Poster

### Mittwoch, 19. März 2014, 16:30–18:30, Spree-Palais

**Perturbative Hydrodynamics of 1d Bose-Einstein Condensate with Ring Geometry in Weak Disorder Potential** — Davron Abdullaev^{1}, Bakhodir Abdullaev^{1}, •Branko Nikolić^{2}, and Axel Pelster^{3} — ^{1}Institute of Applied Physics, National University of Uzbekistan, Tashkent, Uzbekistan — ^{2}Department of Physics, Freie Universität Berlin, Germany — ^{3}Fachbereich Physik und Forschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Germany

The hydrodynamic properties of a dilute stationary Bose-Einstein condensate are determined from solving the coupled continuity and Euler equations. Here we develop a perturbative solution approach by assuming that the disorder potential is weak. In this way we find explicit expressions for the ensemble averages of both the condensate and the superfluid density as well as of the superfluid velocity for a Lorentzian correlated disorder. In the special case of a delta correlated disorder in 3d the results reduce to the ones derived originally by Huang and Meng [1-4]. Furthermore, we specialize our results to Bose-Einstein condensates with a quasi 1d ring geometry which have been experimentally realized in different laboratories worldwide. In particular, we discuss how the ring length affects the respective hydrodynamic properties.

[1] K. Huang, H.-F. Meng, Phys. Rev. Lett. **69**, 644 (1992)

[2] C. Krumnow and A. Pelster,
Phys. Rev. A **84**, 021608(R) (2011)

[3] B. Abdullaev and A. Pelster, Europ. Phys. J. D **66**, 314 (2012)

[4] B. Nikolic, A. Balaz, and A. Pelster, Phys. Rev. A **88**, 013624 (2013)