The field of ultracold atomic gases provides a new opportunity for the investigation of the quantum properties of matter. The rapid progress of both experimental and theoretical research in the past three decades has facilitated an astonishing insight at the level of few atoms as well as large ensembles. This work examines the usage of dispersive, magnetically sensitive, optical probing for high resolution detection of the cold atomic clouds. This minimally destructive online measurement technique is utilized in a feedback scheme, which can actively stabilize the sample production to the level of atom shot noise. In addition, experiments with spinor condensates in a one dimensional vertical optical lattice are presented, where spin changing collisions generating wave packet like excitations with anti-correlated momenta are observed. The theoretical part of the book considers a proposal for a two-qubit quantum gate (controlled-NOT) operating on motional degrees of freedom of atoms trapped in a super-lattice potential. It also examines the limits of time evolution of quantum systems in the theoretical framework of Hilbert space geometry.