Entanglement Creation in Low-Energy Scattering

TL;DR

This paper rigorously analyzes how low-energy scattering of two particles creates entanglement, showing the dependence on mass difference and the negligible effect of potential anisotropy on leading order purity.

Contribution

It provides an explicit, error-bounded computation of the leading order entanglement measure in low-energy scattering for general, non-spherically symmetric potentials.

Findings

Entanglement increases with mass difference.

Minimum entanglement occurs when masses are equal.

Potential anisotropy does not affect leading order purity.

Abstract

We study the entanglement creation in the low-energy scattering of two particles in three dimensions, for a general class of interaction potentials that are not required to be spherically symmetric. The incoming asymptotic state, before the collision, is a product of two normalized Gaussian states. After the scattering the particles are entangled. We take as a measure of the entanglement the purity of one of them. We provide a rigorous explicit computation, with error bound, of the leading order of the purity at low-energy. The entanglement depends strongly in the difference of the masses. It takes its minimum when the masses are equal, and it increases rapidly with the difference of the masses. It is quite remarkable that the anisotropy of the potential gives no contribution to the leading order of the purity, on spite of the fact that entanglement is a second order effect.