  For a Bose Josephson junction realized with a double-well potential we
propose a strategy to observe the coherent superpositions of phase states
occurring during the time evolution after a sudden rise of the barrier
separating the two wells. We show that their phase content can be obtained by
the full-counting statistics of the spin-boson operators characterizing the
junction, which could be mapped out by repeated measurements of the population
imbalance after rotation of the state. This measurement can distinguish between
coherent superpositions and incoherent mixtures, and can be used for a
two-dimensional, tomographic reconstruction of the phase content of the state.
