Statistical signatures of states orthogonal to the Fock-state ladder of composite bosons

The theory of composite bosons (cobosons) made of two fermions [C. K. Law, Phys. Rev. A 71, 034306 (2005); M. C. Tichy et al., 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 $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}$ of a composite boson couples the $N$-coboson Fock state not only to the $(N\ensuremath{-}1)$-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 us to extract the 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.