Spin Squeezing In Bose-Einstein Condensates

Spin squeezed states are multi-particle entangled states that have practical interest in quantum metrology and atomic interferometer. In this thesis, we study theoretically realistic schemes for the production of spin squeezed states using the coherent interactions between cold atoms in a bimodal Bose-Einstein condensate. In particular, we include decoherence process such as particle losses, as well as spatial dynamics which limit the maximum squeezing reachable in a real experiment. We find that the effect of losses cannot be neglected as soon as the lost fraction of particles is of the order of the squeezing parameter. The analytical solution that we find, using Monte-Carlo wave functions approach, allows us to perform an optimization for the spin squeezing with respect to the experiment parameters. The method that we develop to study the entangled spatial and spin dynamics of interacting bimodal BEC allows a full analytical treatment for spin squeezing in some cases and can be used in the general case without the need of heavy numerics. We apply our theoretical studies to an experiment for spin squeezing recently realized successfully on an atom chip. Finally, we study the spin squeezing in a related but different system of a BEC with two external modes coherently coupled by the tunnel effect. We study this problem with a dynamical two-mode model for T (?) Tc and within a multimode approach in thermal equilibrium for T(?)Tc.