Role of fermion exchanges in statistical signatures of composite bosons

We study statistical signatures of composite bosons made of two fermions by extending number states to these quantum particles. Two-particle correlations as well as the dispersion of the probability distribution are analyzed. We show that the particle composite nature reduces the antibunching effect predicted for elementary bosons. Furthermore, the probability distribution exhibits a dispersion that is greater for composite bosons than for elementary bosons. This dispersion corresponds to the one of sub-Poissonian processes, as for a quantum state but, unlike its elementary boson counterpart, it is not minimum. In general, our work shows that it is necessary to take into account the Pauli exclusion principle, which acts between fermionic components of composite bosons---along the line used here---to possibly extract statistical properties in a precise way.