  The theory of composite bosons (cobosons) made of two fermions [Phys. Rev. A
71, 034306 (2005), Phys. Rev. Lett. 109, 260403 (2012)] converges to ordinary
structureless bosons in the limit of infinitely strong entanglement between the
fermionic constituents. For finite entanglement, the annihilation operator
$\hat c$ of a composite boson couples the $N$-coboson Fock-state not only to
the $(N-1)$-coboson state -- as for ordinary bosons --, but also to a component
which is orthogonal to the Fock-state ladder of cobosons. Coupling with states
orthogonal to the Fock ladder arises also in dynamical processes of cobosons.
Here, with a Gedanken-experiment involving both mode-splitting and collective
Hong-Ou-Mandel-like interference, we derive the characteristic physical
signature of the states orthogonal to the Fock ladder generated in the
splitting process. This allows to extract microscopic properties of
many-fermion-wave functions from the collective coboson behavior. We show that
consecutive beam-splitter dynamics increases the deviation from the ideal
bosonic behavior pattern, which opens up a rigorous approach to the
falsification of coboson theory.
