Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to   Bose-Einstein Condensate
  We study an ultracold Bose gas in the presence of 1D disorder for repulsive inter-atomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes. 
Pierre Lugan (LCFIO), David Cl\'ement (LCFIO), Philippe Bouyer   (LCFIO), Alain Aspect (LCFIO), Maciej Lewenstein (ICFO), La...