Quantum Entanglement Control in Two-Spin-1/2 NMR Systems Through Magnetic Fields and Temperature

TL;DR

This paper analyzes how magnetic fields and temperature influence quantum entanglement in two-spin-1/2 NMR systems, deriving analytical expressions and criteria for quantum critical points, and linking entanglement to NMR observables for practical measurement.

Contribution

It provides the first analytical expressions for entanglement dependence on temperature and magnetic fields in NMR systems, and introduces criteria for quantum critical points applicable to various settings.

Findings

Entanglement vanishes above a threshold temperature.

Zero-temperature system exhibits a quantum critical point.

Entanglement can be quantified through NMR signal processing.

Abstract

We investigate quantum entanglement in two-spin-1/2 NMR systems at thermal equilibrium under external magnetic fields. We derive closed-form analytical expressions for the entanglement of the system and show how the entanglement depends on temperature and magnetic field strength, resulting in a threshold temperature beyond which entanglement vanishes. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measure of entanglement. We further develop analytical criterion for level crossing, which serves as a condition for identifying quantum critical points in both homonuclear and heteronuclear systems, and apply it to multiple settings to analyze their quantum critical points. We establish a direct link between the quantum entanglement quantifier and experimentally accessible NMR observables, enabling entanglement to be quantified through NMR signal processing. This provides a practical framework for characterizing quantum correlations using standard NMR experiments. These findings provide insights into the thermal control of quantum features, with implications for quantum-enhanced NMR, low-temperature spectroscopy, and emerging quantum technologies.