• Bose-Einstein Condensation
• Mott Insulator
• Optical Lattice
• Tunneling

Since the early days of quantum mechanics ”toy models” have been used to explain and teach the counterintuitive phenomena of the quantum world.
The experimental realization of quantum degenerate states in ultracold
atoms gases in the 1990’s has opened the possibility to have few body systems
isolated from external perturbations and at temperatures close to absolute zero. Under these conditions the Heisenberg indetermination principle becomes the only limit. Different tools have been developed for the study of
dynamic behavior (i.e. for simulation of vortices in superfluidity) and of spatially
periodic systems (i.e. for the simulation of crystals). These techniques allow physicists to manipulate a small number of quantum particles and to use them in a huge variety of experiments where it is possible to measure and characterize fundamental phenomena. For example, astounding examples were achieved in the last ten years by using optical lattices in the study of tunneling. The possibility of easily changing the parameters (depth, lattice constant etc.) of a defect-free potential permits one to observe, for example,
Bloch oscillations and the quantum phase transition into a Mott-insulator
regime. An interesting subject that has not been studied extensively in experiments
so far is that of strongly driven quantum systems, where a timedependent (in particular periodic) perturbation is introduced in the system in order to probe it or to change its fundamental properties. The theoretical
approach for these phenomena includes the external driving inside one of the
parameter of the unperturbed system similarly to what is done in solid state physics for the renormalizazion of the mass of an electron in a crystal. The parameter becomes variable and the problem can be treated in a easier way. In this thesis I will present the results obtained concerning the possibility to adiabatically modify the quantum process of tunneling using an external periodical forcing on the optical potential. By periodically moving the lattice
backwards and forwards, the fundamental tunneling properties of the atoms inside the lattice can be adiabatically changed and the system can be carried into novel regimes impossible to reach with static techniques. In particular,
for our system the renormalization approach needs to be expanded to a macroscopic coherent ensemble of atoms and it becomes natural to refer to
it as a dressed matter wave. I will show how this idea can be realized and the matter waves can be adiabatically dressed without losing the quantum coherence of the ensemble also during a quantum phase transition.