The topic of this thesis is the study of localization of a quasi-one-dimensional and harmonically trapped Bose-Einstein condensate through which various disordered potentials are transported. This problem, which wants itself to be fully relevant to experimenters, is a priori difficult to deal with. This is due to the non-linear, inhomhogeneous and out-of-equilibrium nature of the system. Because of this, the range of speeds of disorder is limited on one side by the critical speed of superfluidity and on the other side by the inhomogeneous setting of the system. Usual notions of localization like transmission and Lyapunov exponent are no longer applicable. Thus, we had to introduce a novel measure of localization for our problem: the ratio of the distance moved by the condensate center of mass to the distance moved by the disordered potential that we identify as the fraction of localized atoms. Furthermore, we have correlations in the disorder that introduce the effect of non-monotonic behavior of the localization efficiency of the disordered potential as a function of energy. A a result, correlations can be used as a tool to point the quantum nature of the localization. We did this in a first part with Edwards Model type disorders and in a second part with speckle type disorders, a new one that we call the Random Dimer speckle. For this second part, we propose a scheme to control the correlations and introduce a localization peak in a certain energy region. This device can be verified in experiments with the help of a Spatial Light Modulator.
