Boundary between the thermal and statistical polarization regimes in a nuclear spin ensemble

TL;DR

This paper investigates the transition from thermal to statistical polarization in nanometer-scale nuclear spin ensembles using magnetic resonance force microscopy, providing insights into the polarization regimes at extremely small detection volumes.

Contribution

It experimentally measures the boundary between thermal and statistical polarization regimes in nanometer-scale nuclear spin ensembles, advancing understanding of polarization behavior at small scales.

Findings

Identified the transition point between polarization regimes.

Quantified the number of spins in nanometer-scale ensembles.

Demonstrated measurement technique for polarization regimes.

Abstract

As the number of spins in an ensemble is reduced, the statistical uctuations in its polarization eventually exceed the mean thermal polarization. This transition has now been surpassed in a number of recent nuclear magnetic resonance experiments, which achieve nanometer-scale detection volumes. Here, we measure nanometer- scale ensembles of nuclear spins in a KPF6 sample using magnetic resonance force microscopy. In particular, we investigate the transition between regimes dominated by thermal and statistical nuclear polarization. The ratio between the two types of polarization provides a measure of the number of spins in the detected ensemble.