# Stuttgart 2012 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 34: Poster 1

### Q 34.10: Poster

### Dienstag, 13. März 2012, 16:30–19:00, Poster.I+II

**Condensate Depletion due to Correlated Disorder** — •Christopher Gaul^{1} and Cord A. Müller^{2} — ^{1}GISC, Departamento de Física de Materiales, Universidad Complutense, E-28040 Madrid, Spain — ^{2}Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore

We study interacting bosons at low temperature in spatially correlated disorder potentials. In the noninteracting case all particles condense into the lowest single-particle state. Due to interactions, however, a certain fraction of particles is outside the condensate, even at zero temperature and in the homogeneous case.

The Bogoliubov ansatz splits Ψ(** r**) into the (mean-field) condensate Φ(

**) and the quantum fluctuations δ ψ(**

*r***). In the first step one neglects the quantum fluctuations. The Gross-Pitaevskii equation describes how the condensate is deformed by the disorder potential. This is not yet a depletion of the condensate mode, which is still populated by all particles. We then consider the quantum fluctuations. By a Bogoliubov expansion around the deformed mean-field condensate, we derive the fundamental Hamiltonian for elementary excitations, including an analytical formulation in the case of weak disorder. From this, we calculate the sound velocity as well as the quantum depletion of the condensate due to interaction and disorder. We cover the relevant dimensions**

*r**d*=1,2,3 and arbitrary correlation lengths, including the limit of uncorrelated disorder.

C. Gaul and C.A. Müller PRA, 83, 063629 (2011)

C. Gaul and C.A. Müller arXiv:1009.5448