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We formulate a semiclassical approach to study the dynamics of coherence lossand revival in a Bose-Josephson dimer. The phase-space structure of thebi-modal system in the Rabi, Josephson, and Fock interaction regimes, isreviewed and the prescription for its WKB quantization is specified. The localdensity of states (LDOS) is then deduced for any given preparation from itssemiclassical projection onto the WKB eigenstates. The LDOS and the non-linearvariation of its level-spacing are employed to construct the time evolution ofthe initial preparation and study the temporal fluctuations of interferometricfringe visibility. The qualitative behavior and characteristic timescales ofthese fluctuations are set by the pertinent participation number, quantifyingthe spectral content of the preparation. We employ this methodology to studythe Josephson-regime coherence dynamics of several initial state preparations,including a Twin-Fock state and three different coherent states that we denoteas 'Zero', 'Pi', and 'Edge' (the latter two are both on-separatrixpreparations, while the Zero is the standard ground sate preparation). We finda remarkable agreement between the semiclassical predictions and numericalsimulations of the full quantum dynamics. Consequently, a characteristicdistinct behavior is implied for each of the different preparations.

Temporal quantum fluctuations in the fringe-visibility of atom interferometers with interacting Bose-Einstein condensate