Bosonic behavior of entangled fermions

Abstract

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure from ideal bosonic behavior is quantified by the normalization ratio of $N$-composite-boson states. We derive the two-fermion states that extremize the normalization ratio for a fixed single-fermion purity $P$, and establish general tight bounds for this indicator. For very small purities, $P<1/{N}^{2}$, the upper and lower bounds converge, which allows us to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.