Detection of coherent superpositions of phase states by full counting statistics in a Bose Josephson junction

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.