  Nitrogen-vacancy (NV) centers in diamond can be used as quantum sensors to
image the magnetic field with nanoscale resolution. However, nanoscale
electric-field mapping has not been achieved so far because of the relatively
weak coupling strength between NV and electric field. Using individual shallow
NVs, here we succeeded to quantitatively image the contours of electric field
from a sharp tip of a qPlus-based atomic force microscope (AFM), and achieved a
spatial resolution of ~10 nm. Through such local electric fields, we
demonstrated electric control of NV's charge state with sub-5 nm precision.
This work represents the first step towards nanoscale scanning electrometry
based on a single quantum sensor and may open up new possibility of
quantitatively mapping local charge, electric polarization, and dielectric
response in a broad spectrum of functional materials at nanoscale.
