Magnetic resonance force microscopy of nuclear spins: Detection and manipulation of statistical polarization

We have detected and manipulated the naturally occurring √N statistical polarization in nuclear spin ensembles using magnetic resonance force microscopy. Using protocols previously developed for detecting single electron spins, we have measured signals from ensembles of nuclear spins in a volume of roughly (1500.3em0exnm)³ with a sensitivity of roughly 2000 net spins in a 2.50.3em0exh averaging window. Three systems have been studied, ¹⁹F nuclei in CaF₂, and ¹H nuclei (protons) in both polymethylmethacrylate and collagen, a naturally occurring protein. By detecting the statistical polarization, we not only can work with relatively small ensembles, but we eliminate any need to wait a longitudinal relaxation time T₁ to polarize the spins. We have also made use of the fact that the statistical polarization, which can be considered a form of spin noise, has a finite correlation time. A method similar to one previously proposed by Carlson et al. [Bull. Am. Phys. Soc. 44, 541 (1999)] has been used to suppress the effect of the statistical uncertainty and extract meaningful information from time-averaged measurements. By implementing this method, we have successfully made nutation and transverse spin relaxation time measurements in CaF₂ at low temperatures.