Entanglement of magnetic impurities through electron scattering in an electric field

We show that the entanglement between two distant magnetic impurities, generated via electron scattering, can be easily modulated by controlling the magnitude of an applied external electric field. We assume that the two magnetic impurities are fixed and located on an one-dimensional quantum wire. A ballistic electron moving through the wire is scattered off by both impurities, so the electron spin can be seen as a mediator between the spins of the impurities. Heisenberg operators are used to describe the interactions between electron and impurities spins. We use a wave guide formalism to model the ballistic electron wave function. Entanglement control is shown to be possible for three different protocols of entanglement detection. The effect of detection protocols on the entanglement extraction is discussed.