  Squeezed states and macroscopic superpositions of coherent states have been
predicted to be generated dynamically in Bose Josephson junctions. We solve
exactly the quantum dynamics of such a junction in the presence of a classical
noise coupled to the population-imbalance number operator (phase noise),
accounting for, for example, the experimentally relevant fluctuations of the
magnetic field. We calculate the correction to the decay of the visibility
induced by the noise in the non-Markovian regime. Furthermore, we predict that
such a noise induces an anomalous rate of decoherence among the components of
the macroscopic superpositions, which is independent of the total number of
atoms, leading to potential interferometric applications.
