Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments

TL;DR

This paper theoretically investigates quantum correlations, including entanglement and discord, in two-spin NMR systems under different multiple-pulse spin-locking schemes, revealing conditions for their emergence at various temperatures.

Contribution

It introduces a theoretical analysis of quantum correlations in NMR spin-locking experiments with two different pulse schemes, highlighting conditions for entanglement and discord.

Findings

Entanglement is absent in the first scheme at equal delays.

Entanglement appears in the second scheme at low temperatures.

Quantum discord is present across different temperatures.

Abstract

Quantum correlations are investigated theoretically in a two-spin system with the dipole-dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of $\pi/2$-pulses only and the delays between the pulses can differ. The second scheme contains $\varphi$-pulses ($0<\varphi<\pi$) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between $\pi/2$-pulses at arbitraty temperatures. Entanglement emerges after several periods of the pulse sequence in the second scheme at $\varphi=\pi/4$ at milliKelvin temperatures. The necessary number of the periods increases with increasing temperature. We demonstrate the dependence of entanglement on the number of the periods of the multiple-pulse sequence. Quantum discord is obtained for the first scheme of the multiple-pulse spin-locking experiment at different temperatures.