Abstract

The aims of this dissertation are twofold. Firstly, the study of superfluidity, presented in the first part, has more a fundational character, since we investigate some well known problems, already raised in the context of superfluid helium, in order to gain a deeper understanding, by exploiting the cleannes of dilute BECs systems, as well as analyzing the new features emerging from the unique dilute BECs properties. We study the BEC flow through weak-links, first analyzing the various regimes of transport by the current-phase relation and the Josephson plasma oscillations, and then turning to the superfluid instability, determining critical velocities and examining the dissipation dynamics in different geometries and dimensionalities. Secondly, the analysis of quantum interferometry, given in the second part, has instead a more technological character, since we propose two possible implementation of interferometric protocols in double-well traps, with application to the measurement of weak-forces, and study their sensitivity in detail, especially in relation to its possible quantum enhancement.