Interacting Bosons in optical lattices: optimal control ground state production, entanglement characterization and 1D systems

The work presented in this thesis concerns the study of quantum many-body physics by making use Bose-Einstein condensates loaded in optical lattices potentials. The first part describes the development of a new experimental strategy for the production of the degenerate atomic sample, the second part concerns the optimal control ground state production and the entanglement characterization on a systems of interacting Bosons across the superfluid - Mott insulator quantum phase transition, and the third part illustrates the study of the dynamical properties of an array of 1D gases performed via Bragg spectroscopy.