Correlated noise in Brownian motion allows for super resolution.

Diffusion broadening of spectral lines is the main limitation to frequency resolution in non-polarized liquid state nano-NMR. This problem arises from the limited amount of information that can be extracted from the signal before losing coherence. For liquid state NMR as with most generic sensing experiments, the signal decays exponentially which limits resolution severely. In this work we show that unlike in the generic case, diffusion noise in the NV based nano-NMR setup inflicts a power law decay of the signal resulting in high spectral resolution.