In realistic electronic nanograins this goal is far away of being fulfilled in part because it is hard to asses the impact of interactions and its role in the loss of quantum coherence.
Ultra cold atoms confined by optical potentials offer a better option. The strength of the interactions, disorder and the form of the confining potential can be controlled with great precision. In addition it is possible to search for new physics by further lowering down the temperature.
This a challenge for theorists: develop models that can be verified so accurately that a discrepancy with experiments may mean new physics!. Motivated by such exciting possibilities, my research is a response to these challenges. It is organized around three broad objectives:
Develop a theoretical framework to describe how the properties
of a system confined in a clean grain depend on its size and form. The
motivation is mainly practical. I anticipate that in the context of
superconductivity it would permit design superconducting nanograins
with an unusually high critical temperature. In the context of bosonic
gases such a study its of relevance in industrial applications aimed to
manufacture cavities of a given size and shape as it would determine
exactly to what extent the form of a real cavity deviates from some
given "ideal" geometry.
Develop theoretical models to describe Anderson localization in ultra cold atoms. By Anderson localization it is meant the total suppression of classical diffusion in a random potential due to quantum interference effects. This is a purely quantum effect with no classical analogous. The aim is to develop an theory of localization adapted to the peculiarities of almost free ultracold atoms in speckle (or kicked) potentials accurate enough such that it can be used to test quantum mechanics itself.