  Nitrogen vacancy (NV) centers in diamond have been used as ultrasensitive
magnetometers to perform nuclear magnetic resonance (NMR) spectroscopy of
statistically polarized samples at 1 - 100 nm length scales. However, the
spectral linewidth is typically limited to the kHz level, both by the NV sensor
coherence time and by rapid molecular diffusion of the nuclei through the
detection volume which in turn is critical for achieving long nuclear coherence
times. Here we provide a blueprint for a set-up that combines a sensitivity
sufficient for detecting NMR signals from nano- to micron-scale samples with a
spectral resolution that is limited only by the nuclear spin coherence, i.e.
comparable to conventional NMR. Our protocol detects the nuclear polarization
induced along the direction of an external magnetic field with near surface NV
centers using lock-in detection techniques to enable phase coherent signal
averaging. Using NV centers in a dual role of NMR detector and optical
hyperpolarization source to increase signal to noise, and in combination with
Bayesian interference models for signal processing, nano/microscale NMR
spectroscopy can be performed on sub-millimolar sample concentrations, several
orders of magnitude better than the current state of the art.
