Emergence of intraparticle entanglement and time-varying violation of Bell's inequality in Dirac matter

Bruna Gabrielly De Moraes,Aron W Cummings,Stephan Roche

doi:10.1103/physrevb.102.041403

Abstract

We demonstrate the emergence and dynamics of intraparticle entanglement in massless Dirac fermions. This entanglement, generated by spin-orbit coupling, arises between the spin and sublattice pseudospin of electrons in graphene. The entanglement is a complex dynamic quantity but is generally large, independent of the initial state. Its time dependence implies a dynamical violation of a Bell inequality, while its magnitude indicates that large intraparticle entanglement is a general feature of graphene on a substrate. These features are also expected to impact entanglement between pairs of particles, and may be detectable in experiments that combine Cooper pair splitting with nonlocal measurements of spin-spin correlation in mesoscopic devices based on Dirac materials.

Highlights

The importance of quantum entanglement was sparked by the seminal gedanken experiment proposed in 1935 by Einstein et al [1], who in an attempt to demonstrate the incompleteness of quantum mechanics inspired the study of nonlocal correlations between distant particles [1,2,3]
Its time dependence implies a dynamical violation of a Bell inequality, while its magnitude indicates that large intraparticle entanglement is a general feature of graphene on a substrate
We have shown that intraparticle entanglement in graphene is a complex dynamic quantity, governed by the mutual precession of spin and pseudospin

Summary

Rapid Communications

Emergence of intraparticle entanglement and time-varying violation of Bell’s inequality in Dirac matter. We demonstrate the emergence and dynamics of intraparticle entanglement in massless Dirac fermions. This entanglement, generated by spin-orbit coupling, arises between the spin and sublattice pseudospin of electrons in graphene. Its time dependence implies a dynamical violation of a Bell inequality, while its magnitude indicates that large intraparticle entanglement is a general feature of graphene on a substrate. These features are expected to impact entanglement between pairs of particles, and may be detectable in experiments that combine Cooper pair splitting with nonlocal measurements of spin-spin correlation in mesoscopic devices based on Dirac materials

Introduction

In this basis the eigenstates of the Hamiltonian are

Discussion and conclusions