Observation of Non-Gaussian Statistics and Levy Flights in Nitrogen Vacancy Centers

A nitrogen-vacancy center can be used as a probe of the interacting $^{\mathrm{13}}$C nuclear spins in a diamond crystal. Under the right conditions, its behavior can be described as a random walk with step sizes drawn from a distribution without a well-defined mean or standard deviation. Its behavior is then described by Levy statistics, providing an opportunity to study Levy statistics in a well understood system.