  We demonstrate three-dimensional magnetic resonance tomography with a
resolution down to 5.99 +- 0.07 nm. Our measurements use lithographically
fabricated microwires as a source of three-dimensional magnetic field
gradients, which we use to image NV centers in a densely doped diamond by
Fourier-accelerated magnetic resonance tomography. We also present a compressed
sensing scheme for imaging of a spatially localized ensemble from undersampled
data, which allows for a direct visual interpretation without numerical
optimization. The resolution achieved in our work approaches the positioning
accuracy of site-directed spin labeling, paving the way to three-dimensional
structure analysis by magnetic-gradient based tomography.

Quantum Physics