  When probing nuclear spins in materials on the nanometer scale, random
fluctuations of the spin polarization will exceed the mean Boltzmann
polarization for sample volumes below about (100nm)^3. In this work, we use
magnetic resonance force microscopy to observe nuclear spin fluctuations in
real time. We show how reproducible measurements of the polarization variance
can be obtained by controlling the spin correlation time and rapidly sampling a
large number of independent spin configurations. A protocol to periodically
randomize the spin ensemble is demonstrated, allowing significant improvement
in the signal-to-noise ratio for nanometer-scale magnetic resonance imaging.
