Heating effects and localization mechanism in cold Bose gases

Collapse models solve the measurement problem by adding non-linear and stochastic terms to the usual Schroedinger dynamics. The resulting dynamics localizes in position macroscopic systems, while preserves quantum mechanical predictions for microscopic systems. Two of the main consequences of this resulting dynamics are: the loss of any initial spatial coherence, with a decoherence rate which increases with the dimensions of the system (amplification mechanism); and a heating effect induced on the system that, for long times, leads either to a divergent or to a convergent value of the energy, depending on the particular collapse model considered. An interesting class of system to experimentally test collapse models are cold atomic gases. Besides their very low temperatures (T = 10^(-11) - 10^(-7)K), cold atomic gases show mesoscopic quantum properties, i.e. involving a number of atoms of order of N = 10^(3)– 10^(11). These are all necessary ingredients to experimentally test collapse models. In this thesis, we use cold bosonic atomic gas to test one of the most studied and complete among collapse models, i.e. CSL, and also its non-Markovian and dissipative extensions. In particular, in this thesis we put bounds on CSL free-parameters by studying the diffusion effect induced by collapse noise on a free expanding gas, and we compare the theoretical results with experimental data known in literature. The bounds we put are among the strongest ever found non only for CSL model, but especially for its non-Markovian extension. In this thesis we also specialize the CSL dynamics in Bose-Josephson junctions, and we focus on the localization mechanism induced by the noise on initially entangled states. In particular, we focus on decoherence induced by CSL on typical entangled states as atomic coherent states and NOON states. We find that in the latter ones, CSL effects become significant when the NOON state is composed by a number of atoms of 10^(4) or greater. Moreover, we compare CSL decoherence with environmental decoherence induced by typical realistic sources, as an external thermal cloud, imperfections in the trapping laser, and three body effects. We then find which conditions experiments must fulfill in order to test CSL in a Bose-Josephson junction in conditions never