  We numerically study the classical and quantum dynamics of an atomic bright
soliton in a highly-elongated one-dimensional harmonic trap with a Gaussian
barrier. In the regime of the recent experiment by Dyke {\it et al.}, the
system realizes a coherent nonlinear soliton beam-splitter and interferometer
whose accuracy we analyze. In the case of tighter radial trap confinement and
enhanced quantum fluctuations, a split soliton can represent a spin-squeezed,
or alternatively, a fragmented condensate with reduced phase-coherence that can
be measured by interfering the split soliton by the barrier. We also find large
quantum mechanical uncertainties in the soliton's position and momentum due to
nonlinear interaction with the barrier.
