Screening effect and delocalization of interacting Bose-Einstein condensates in random potentials
Résumé
We theoretically investigate the physics of interacting Bose-Einstein condensates at equilibrium in a weak (possibly random) potential. We develop a perturbation approach to derive the condensate wavefunction for an amplitude of the potential smaller than the chemical potential of the condensate and for an arbitrary spatial variation scale of the potential. Applying this theory to disordered potentials, we find in particular that, if the healing length is smaller than the latter, the condensate assumes a delocalized Thomas-Fermi profile. In the opposite situation where the typical variation scale of the potential is smaller than the healing length, we show that the random potential can be significantly screened and, in the meanfield regime, the condensate wavefunction can remain delocalized, even for very small correlation lengths of the disorder.