  We predict hyper-entanglement generation during binary scattering of
mesoscopic bound states, solitary waves in Bose-Einstein condensates containing
thousands of identical Bosons. The underlying many-body Hamiltonian must not be
integrable, and the pre-collision quantum state of the solitons fragmented.
Under these conditions, we show with pure state quantum field simulations that
the post-collision state will be hyper-entangled in spatial degrees of freedom
and atom number within solitons, for realistic parameters. The effect links
aspects of non-linear systems and quantum-coherence and the entangled
post-collision state challenges present entanglement criteria for identical
particles. Our results are based on simulations of colliding quantum solitons
in a quintic interaction model beyond the mean-field, using the truncated
Wigner approximation.
