  In a two-mode Bose Josephson junction the dynamics induced by a sudden quench
of the tunnel amplitude leads to the periodic formation of entangled states.
For instance, squeezed states are formed at short times and macroscopic
superpositions of phase states at later times. The two modes of the junction
can be viewed as the two arms of an interferometer; use of entangled states
allows to perform atom interferometry beyond the classical limit. Decoherence
due to the presence of noise degrades the quantum correlations between the
atoms, thus reducing phase sensitivity of the interferometer. We consider the
noise induced by stochastic fluctuations of the energies of the two modes of
the junction. We analyze its effect on squeezed states and macroscopic
superpositions and study quantitatively the amount of quantum correlations
which can be used to enhance the phase sensitivity with respect to the
classical limit. To this aim we compute the squeezing parameter and the quantum
Fisher information during the quenched dynamics. For moderate noise intensities
we show that these useful quantum correlations increase on time scales beyond
the squeezing regime. This suggests multicomponent superpositions as
interesting candidates for high-precision atom interferometry.
