Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments

TL;DR

This paper explores how entanglement evolves in multiple-quantum NMR experiments with nuclear spin pairs, establishing a link between entanglement measures and MQ coherence intensities, and proposing an entanglement witness.

Contribution

It introduces a simple condition for entanglement emergence and demonstrates that MQ NMR coherences can be used to study spin entanglement qualitatively.

Findings

Entanglement correlates with MQ coherence intensities.

A simple criterion for entanglement emergence is proposed.

An entanglement witness based on MQ coherences is introduced.

Abstract

We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear spins-1/2. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the non-secular part of the dipolar Hamiltonian. As a result, MQ coherences of the zeroth and plus/minus second orders appear. A simple condition for the emergence of entanglement is obtained. We show that the measure of the spin pair entanglement, concurrence, coincides qualitatively with the intensity of MQ coherences of the plus/minus second order and hence the entanglement can be studied with MQ NMR methods. We introduce an Entanglement Witness using MQ NMR coherences of the plus/minus second order.