Noisy effects in ultracold atomic gases

The experimental realization of Bose Einstein Condensates opened the path for a wide range of investigations in physics of ultracold atoms; the peculiar characteristics of these systems and the recent advances in optical con?nement technology make them preferred candidates for the implementation of quantum communication and information protocols based on many-body coherent states. In this framework, the dissertation focuses on some consequences that the presence of a weakly coupled external environment has on a system of cold atoms in an optical trap. Typically, the presence of an environment leads to noise and dissipation; whereas the thesis investigates the capability of the environment of mediating an induced interaction between otherwise isolated atoms, making possible the rising of coherence between atoms localized in different sites of the con?ning potential. The effects of this coherence can be interpreted in terms of an atomic current ?owing across the system. Standard open quantum systems methods, mainly related to the weak coupling limit, have been used in order to describe the dissipative dynamics by means of a memoryless master equation. Except for some special cases, this master equation cannot be analitically integrated; therefore, suitable techniques have been used to describe the coherence behaviour at small times, which are of the order of the characteristic times of the dissipative phenomena in the thesis. In detail, the weak coupling limit has been reviewed in the general formalism of open quantum systems; then, after a brief introduction about the physycs of ultracold atoms, the master equation ruling the dissipative dynamics in the presence of a weakly coupled environment, typically a heat bath or a stochastic classical ?eld, has been derived. Two different kinds of coupling have been considered, mainly differing in the conservation of the total number of particles. Having obtained the master equation, which depends on typical phenomenological parameters relative to the environment, the cases in which a dissipative induced current arises as a consequence of the coupling with the environment, have been examined. The effects of this current have been shown to be, in principle, experimentally accessible by looking at absorption images of the freely expanding atomic cloud once the trapping potential has been switched off. From these images it is possible to extract a spatial density pro?le after the free expansion; the presence of interference fringes in this density pro?le denotes the presence of coherence in the trapped system. This experimental procedure has been described in the general framework of the quantum measurement theory: from actual experimental evidence, it has been shown that a consistent use of the wave packet reduction principle leads to theoretical predictions for the expected density pro?le, which are slightly different from the ones commonly used in the literature. These differences have been brie?y discussed both theoretically and for their possible experimental relevance.