Entanglement and Composite Bosons

TL;DR

This paper investigates how the entanglement between two fermions influences their collective behavior as composite bosons, deriving bounds that connect entanglement measures to bosonic properties.

Contribution

It generalizes previous work by establishing bounds on bosonic behavior based on entanglement, using the purity of the single-particle density matrix.

Findings

Stronger entanglement leads to more ideal bosonic behavior.

Derived bounds depend on the purity of the single-particle density matrix.

Entanglement is a key factor in the bosonic character of fermion pairs.

Abstract

We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity that governs the bosonic character of a pair of fermions when N such pairs approximately share the same wavefunction. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity in question approaches its ideal bosonic value.