[tel-01099521] Dynamique dans un réseau optique conservatif

Optical lattices are structures created by the interference of laser beams, which make it possible to trap and arrange cold atoms. They have become a model system for several domains in physics, because it is possible to simulate other systems by changing the lattice geometry and its parameters. These characteristics are easy to modify experimentally. In particular, it is possible to obtain conservative optical lattices. In this thesis, we study the dynamics of an atom trapped in a 2D conservative optical lattice. The dynamics of the atom depends on the parameters of the lattice, and it is often complex. In consequence, this thesis is at the interface between the domains of cold atoms and non-linear dynamics. The study of the dynamics in the optical lattice needs to be done firstly in the classical limit. We examine in the first place the solutions to the movement equations obtained by numerical integration, for the different configurations of the system. They show a big variety of possible dynamical regimes. Amongst these regimes we find synchronization phenomena leading to a periodic movement locked in frequency. Synchronization seems to inhibit chaos in the system. The main solutions obtained numerically are also studied analytically. This approach allows us to obtain a description of the movement for the different dynamical regimes observed. All these regimes are easy to reproduce experimentally and the influence of synchronization on the existence of chaos needs to be studied. Additionally, this classical analysis serves as a basis for studying the system in the quantum limit.



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