Quantum Entanglement in the Nonrelativistic Collision Between Two Identical Fermions with Spin 1/2

Abstract

In the framework of nonstationary scattering theory, we study the formation of an entangled state of two identical nonrelativistic spin-1/2 particles as a result of their elastic scattering. The measure of particle entanglement in the final channel is described using pair concurrence. For the indicated quantitative criterion, we obtain general expressions in terms of the direct and exchange scattering amplitudes in the cases of pure and mixed spin states of the pair in the initial channel. We consider the violation of Bell’s inequality in the final channel. We show that as a result of a collision between unpolarized particles, a Werner spin state of the pair forms, which is entangled if the singlet component of the angular differential scattering cross section in the center-of-mass reference frame exceeds the triplet component. We use the process of free electron-electron scattering as an example to illustrate the developed formalism.