  We discuss an interferometric scheme employing interference of bright
solitons formed as specific bound states of attracting bosons on a lattice. 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, it 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: By employing
a combination of Bethe ansatz and DMRG based analysis of the dynamics of the
appropriate many-body system, we find that the interferometric fringes persist
even when the center-of-mass kinetic energy of the soliton is above the energy
needed for its complete dissociation into constituent atoms.
