  We propose a protocol to estimate magnetic fields using a single
nitrogen-vacancy (N-V) center in diamond, where the estimate precision scales
inversely with time, ~1/T$, rather than the square-root of time. The method is
based on converting the task of magnetometry into phase estimation, performing
quantum phase estimation on a single N-V nuclear spin using either adaptive or
nonadaptive feedback control, and the recently demonstrated capability to
perform single-shot readout within the N-V [P. Neumann et. al., Science 329,
542 (2010)]. We present numerical simulations to show that our method provides
an estimate whose precision scales close to ~1/T (T is the total estimation
time), and moreover will give an unambiguous estimate of the static magnetic
field experienced by the N-V. By combining this protocol with recent proposals
for scanning magnetometry using an N-V, our protocol will provide a significant
decrease in signal acquisition time while providing an unambiguous spatial map
of the magnetic field.
