Role of spin noise in the detection of nanoscale ensembles of nuclear spins.

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 (100 nm){3}. In this Letter, 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. This allows significant improvement in the signal-to-noise ratio for nanometer-scale magnetic resonance imaging.