  The quantum nature of elementary bosons can be completely erased by using
coherent states known as Glauber states. Here, we consider composite bosons
(cobosons) made of two fermions and look for the possibility to erase the
bosonic quantum nature of the field and the fermionic quantum nature of its
constituents, when the distribution of the coboson Schmidt decomposition is
either flat like Frenkel excitons, or localized like Wannier excitons. We show
that for Frenkel-like cobosons, complete erasure of the field quantum nature is
possible up to a density which corresponds to a sizable fraction of the number
of fermion-pair states making the coboson at hand. At higher density, the Pauli
exclusion principle between fermionic constituents shows up dramatically. It
induces: (i) the decrease of number-operator eigenvalues down to 1 and the
increase of the number-state second-order correlation function up to 2; (ii)
the disappearance of the usual sharp peak in the coherent-state distribution
and the increase of the coherent-state second-order correlation function up to
2. It also is possible to construct number states and coherent states for
Wannier-like cobosons, but their forms are far more complex. Finally, we show
that Pauli blocking makes the coboson coherent states qualitatively different
from the Anderson's ansatz.
