Detection and Manipulation of the Statistical Fluctuations in Nuclear Spin Ensembles Using Magnetic Resonance Force Microscopy

We have detected and manipulated the naturally occurring $\sqrt N $ statistical polarization in nuclear spin ensembles using MRFM. We have studied fluorine nuclei in CaF$_{2}$, as well as protons in the polymer PMMA and the protein collagen. The ensembles studied contained of order 10$^{8}$ nuclear spins, corresponding to volumes of order (200nm)$^{3}$, which resulted in statistical polarizations of order 10$^{4}$ net spins. We have also implemented a scheme similar to one proposed by Weitekamp \textit{et al}, in which we suppressed the effect of the statistical uncertainty so as to extract meaningful information from time-averaged measurements. In this way, we have successfully made nutation and transverse spin relaxation measurements in a nominally unpolarized sample of CaF$_{2}$ at low temperatures.