  We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102,
010403 (2009)] for using the scattering of a quantum matter-wave soliton on a
barrier in order to create a coherent superposition state of the soliton being
entirely to the left of the barrier and being entirely to the right of the
barrier. In that proposal, is was assumed that the scattering is perfectly
elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower
than the chemical potential of the soliton. Here we relax this assumption.
Also, we introduce an interferometric scheme, which uses interference of
soltions, that can be used to detect the degree of coherence between the
reflected and transmitted part of the soliton. Using exact diagonalization, we
numerically simulate a complete interferometric cycle for a soliton consisting
of six atoms. We find that the interferometric fringes persist even when the
center-of-mass kinetic energy of the soliton is above the energy needed for
complete dissociation of the soliton into constituent atoms.
