Decoherence and correlations in systems of trapped ultra-cold quantum gases

Since the achievement of Bose-Einstein condensation (BEC), the progress in matterwave physics has been immense. Among the many recent achievements there is the miniaturization of atom traps, demonstration of the superfluid-Mott insulator quantum-phase transition in optical lattices and the experimental demonstration of the BEC-BCS crossover in ultra-cold gases. Miniaturization of atom traps using micro-structured wires on a chip is one important step towards an on-chip cold-atom device. These so-called \atom chips" provide high control and versatility for trapping and guiding the ultra-cold atomic clouds. Particularly interesting is the use of these microchips to build mesoscopic devices for cold atomic clouds as, for instance, in the case of an atom-cloud interferometer. However, these mesoscopic devices require coherent transport of the atom cloud. A general method to treat decoherence due to current fluctuations in multi-wire atomchip traps is presented in the rst part of this thesis. The decoherence rate Γ shows a strong dependence on the distance between the wire and the atom cloud, r0, scaling as Γ ~ r-4 0 for a single atom waveguide. Considering an interferometer device, a strong dependence of the decoherence rate on the trap geometry is found. Studying many-body eects in ultra-cold quantum gases is another important research eld. Experiments using ultra-cold quantum gases in optical lattices have demonstrated the superuid-Mott insulator quantum phase transition and manybody entanglement. Optical lattices are based on a periodic modulation of the light intensity, generated by retro-reected laser beams. Correlations of the atomic cloud between dierent lattice sites of the optical lattice play a central role in these manybody experiments. The dierent phases of the superuid-Mott insulator system can be characterized by the dierent behavior of the inter-lattice site correlations. There are several numerical methods such as Quantum Monte Carlo (QMC) simulations, Density Matrix Renormalization Group (DMRG) ...