  We investigate finite number effects in collisions between two states of an
initially well defined number of identical bosons with attractive contact
interactions, oscillating in the presence of harmonic confinement in one
dimension. We investigate two $N/2$ atom bound states, which are initially
displaced (symmetrically) from the trap center, and then left to freely evolve.
For sufficiently attractive interactions, these bound states are like those
found through use of the Bethe Ansatz (quantum solitons). However, unlike the
free case, the integrability is lost due to confinement, and collisions can
cause mixing into different bound state configurations. We study the system
numerically for the simplest case of $N=4$, via an exact diagonalization of the
Hamiltonian within a finite basis, investigating left/right number uncertainty
as our primary measure of entanglement. We find that for certain interaction
strengths, a phase matching condition leads to resonant transfer to different
bound state configurations with highly non-Poissonian relative number
statistics.
