Summary form only given. The recent experimental observation of Bose-Einstein condensation (BEC) of trapped, dilute gas of alkali atoms, and their manipulation have opened a new chapter in the physics of systems involving the interplay of macroscopics and quantum coherence. Here, we study the 'secondary' quantum effects, i.e., the quantum corrections to the semi-classical Gross-Pitaevskii equation, for two weakly-linked Bose-Einstein condensates. We hence generalize the Josephson current-phase relations by including the effects of quantum fluctuations of the pertinent observables. Such equations will also describe the quantum fluctuations in the Josephson dynamics between two weakly linked mesoscopic superconducting grains.
Summary form only given.The experimental realizations of Bose-Einstein condensation in an atomic trap stimulated a broad interest in the properties of coherent quantum gases. The comparison of trapped condensates to superfluid Helium suggests the possibility of studying and analyzing the rotational properties of condensates. To observe the superfluidlike relation of an atomic condensate, the creation of vortex states is desirable. In this paper, we propose to employ atom optic techniques to achieve this goal.