Creation of Entanglement between Two Electron Spins Induced by Many Spin Ensemble Excitations

TL;DR

This paper theoretically investigates creating entanglement between two electron spins via a nuclear ensemble, modeling the system with a bosonic mode and using a time-dependent Fröhlich transformation to analyze effective spin interactions.

Contribution

It introduces a novel theoretical approach to generate spin entanglement through collective excitations in a nuclear ensemble using a microscopic bosonic model.

Findings

Maximum entanglement occurs when electron velocity matches initial separation.

Increasing collective excitations reduces the entanglement between spins.

The system models a solid-state cavity QED architecture.

Abstract

We theoretically explore the possibility of creating spin entanglement by simultaneously coupling two electronic spins to a nuclear ensemble. By microscopically modeling the spin ensemble with a single mode boson field, we use the time-dependent Fr\"{o}hlich transformation (TDFT) method developed most recently [Yong Li, C. Bruder, and C. P. Sun, Phys. Rev. A \textbf{75}, 032302 (2007)] to calculate the effective coupling between the two spins. Our investigation shows that the total system realizes a solid state based architecture for cavity QED. Exchanging such kind effective boson in a virtual process can result in an effective interaction between two spins. It is discovered that a maximum entangled state can be obtained when the velocity of the electrons matches the initial distance between them in a suitable way. Moreover, we also study how the number of collective excitations influences the entanglement. It is shown that the larger the number of excitation is, the less the two spins entangle each other.