Nonclassicality Analysis and Entanglement Witnessing in Spin-$1/2$ NMR Systems

TL;DR

This paper explores quantum features like coherence, mixedness, and entanglement in two-spin-1/2 NMR systems at thermal equilibrium, deriving analytical expressions and linking them to experimentally measurable NMR spectra.

Contribution

It provides analytical formulas for quantum measures in NMR systems and introduces an entanglement witness directly linked to NMR observables, facilitating experimental testing.

Findings

Quantum critical point at zero temperature with non-analytic coherence behavior

Sharp peak in mixedness at zero temperature

Entanglement can be witnessed through NMR spectra

Abstract

We investigate quantum features and non-classical nature of two-spin-$1/2$ NMR systems at thermal equilibrium under external magnetic fields. More specifically, using suitable quantifiers, we analyze quantum coherence, mixedness, and entanglement in NMR systems and examine their features within the system. We derive closed-form analytical expressions for the quantum elements and show how they depend on temperature and magnetic field strength. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measures of coherence, and a sharp peak in mixedness. Moreover, we analyze the entanglement of the system using a suitable entanglement witness. This provides an experimentally friendly setting for testing entanglement in NMR systems. In other words, the witness links the entanglement in the system to quantum observables, making it directly provable in NMR experiments. We establish a connection between quantum information quantifiers and experimentally accessible NMR spectra of the system, enabling the quantification of entanglement, coherence, and mixedness through NMR signal processing.