Bosonic behavior of entangled fermions

TL;DR

This paper investigates how entangled fermions form composite bosons and quantifies the conditions under which they behave like ideal bosons, providing bounds on deviations based on entanglement purity.

Contribution

It derives extremal two-fermion states for fixed purity and establishes tight bounds on the bosonic behavior of composite particles.

Findings

Bounds converge for small purities P<1/N^2

Quantifies departure from ideal bosonic behavior

Provides a method to assess bosonic behavior in many-body systems

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 of ideal bosonic behavior is quantified by the normalization ratio of multi-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 to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.