As the number of spins in an ensemble is reduced, the statistical fluctuations 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.
References
In general, and , where denotes an average taken over the detection volume . For detection volumes small enough that is slowly varying throughout, as in all experiments discussed here, .
