Manipulation des Interactions dans les Gaz Quantiques:

The interparticle interactions in ultracold atomic gases can be tuned using Fano–Feshbach scattering resonances, which occur in low–energy collisions between two atoms. These resonances are usually obtained using an external static magnetic field. They turn ultracold atomic gases into an experimental playground for the investigation of novel phases in which Quantum Physics plays a key role. The work presented in this memoir is part of the theoretical effort towards the search for yet unexplored quantum phases. This manuscript is organised in two parts. The first one is devoted to composite bosons formed in a 2D heteronuclear Fermi gas. We characterise the zero–temperature phase diagram and show the gas–crystal phase transition in this system. Our results are promising in view of future experiments with the 6Li–40K mixture. In the second part, we propose an alternative to static–field Fano–Feshbach resonances. The idea is to achieve the coupling by using a resonant microwave magnetic field. Our scheme applies to any atomic species whose ground state is split by the hyperfine interaction. It does not require the use of a static magnetic field. First, these resonances are presented using a simple two–channel model. We then characterise them numerically using our own full–fledged implementation of the coupled–channel approach. Our results yield optimistic prospects for the observation of microwave–induced Fano–Feshbach resonances with the bosonic alkali atoms 23Na, 41K, 87Rb, and 133Cs.