Quantum and classical correlations in the solid-state NMR free induction decay

TL;DR

This paper analytically investigates quantum and classical correlations in the free induction decay of dipolar-coupled solid-state NMR systems, revealing how quantum properties diminish with increasing spin quantum number S.

Contribution

It derives explicit formulas for correlations in multispin systems of arbitrary S, extending understanding of quantum-classical transition in NMR FID.

Findings

Quantum correlations decrease as S increases, disappearing at S→∞.

Classical and quantum correlation dynamics are linked to the FID shape derivative.

Quantum properties persist for finite V, even as S grows large.

Abstract

The free-induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spins ones coincide if there are many quite equivalent nearest neighbors V in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S>1/2 we provide generalized POVM measurement using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S+1) when S is growing up, and quantum properties disappear completely only if S tend to infinity and not in the case when V tend to infinity.