In this thesis I explore the possibility of accelerating adiabatic processes for quantum systems. Experiments are performed with a trapped ultracold gas of Rubidium-87 atoms in two distinct regimes: with a one-dimensional thermal gas that can be considered non-interacting, and with a three-dimensional Bose-Einstein condensate for which interactions are dominant. In the first chapter, I recall some aspects of the theoretical description and important properties of such gases. The second chapter describes the Bose-Einstein condensation apparatus, mainly composed of two magneto-optical traps and a magnetic trap. In the third chapter, this setup is used to demonstrate that adiabatic processes -- in our case, the slow decompression and displacement of the gas -- can be dramatically accelerated by using a proper design of the time-dependent parameters of the system. The theoretical treatment is detailed and is not restricted to trapped gases. It may be applied to other physical systems described by either a linear or nonlinear Schrödinger equation containing a time-dependent harmonic potential. The final chapter is theoretical and not directly related to the others. In it I investigate the effect of disorder correlations on one-dimensional Anderson localization. I show that a degenerate mixture of Rubidium-87 and Potassium-41 atoms is well suited to study the localization-delocalization transition predicted by existing models of correlated disorder.
