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

Effect of phase noise on useful quantum correlations in Bose Josephson junctions