Localization transition in weakly interacting Bose superfluids in one-dimensional quasiperdiodic lattices

Laboratoire Charles Fabry, Institut d’Optique, CNRS, Univ Paris Sud 11,2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France(Dated: January 14, 2015)We study the localization of collective pair excitations in weakly-interacting Bose superfluids inone-dimensional quasiperiodic lattices. The localization diagram is first determined numerically.For intermediate interaction and quasiperiodic amplitude we find a sharp localization transition,with extended low-energy states and localized high-energy states. We then develop an analyticaltreatment, which allows us to quantitatively map the localization transition into that of an effectivemultiharmonic quasiperiodic system.