Cold atoms in a network of light. The Bose Einstein condensate at the proof of decoherence

In this academic probationary report, the author addressed quantum properties of an N-body system of cold atoms at zero temperature, trapped in a periodic potential. This problem is addressed only with bosons. The author presents a mean-field approach to approximately absorb the effect of interactions between atoms. Then, he addresses the system coupling with an environment such as a measurement apparatus, in order to study the precise dynamics described by the Lindblad equation, and, more precisely, to show that it can be formulated again but in terms of a stochastic extension of the mean field. The objective is thus to develop a theoretical framework for the study of a Bose-Einstein condensate with respect to interactions and decoherence processes which are inevitably induced by an external measurement