  Recent advances in engineering and control of nanoscale quantum sensors have
opened new paradigms in precision metrology. Unfortunately, hardware
restrictions often limit the sensor performance. In nanoscale magnetic
resonance probes, for instance, finite sampling times greatly limit the
achievable sensitivity and spectral resolution. We develop a technique for
coherent quantum interpolation that can overcome these problems. Using a
quantum sensor associated with the Nitrogen Vacancy center in diamond, we
experimentally demonstrate that quantum interpolation can achieve spectroscopy
of classical magnetic fields and individual quantum spins with orders of
magnitude finer frequency resolution than conventionally possible. Not only is
quantum interpolation an enabling technique to extract structural and chemical
information from single biomolecules, but it can be directly applied to other
quantum systems for super-resolution quantum spectroscopy.
