  High-precision sensing of vectorial forces has broad impact on both
fundamental research and technological applications such as the examination of
vacuum fluctuations \cite{casimir09rmp} and the detection of surface roughness
of nanostructures \cite{RevModPhys.89.035002}. Recent years have witnessed much
progress on sensing alternating electromagnetic forces for the rapidly
advancing quantum technology -- orders-of-magnitude improvement has been
accomplished on the detection sensitivity with atomic sensors
\cite{Schreppler1486,Shaniv2017,Gilmore673}, whereas precision measurement of
static {electromagnetic} forces lags far behind with the corresponding
long-term stability rarely demonstrated. Here, based on quantum atomic matter
waves confined by an optical lattice, we perform precision measurement of
static {electromagnetic} forces by imaging coherent wave mechanics in the
reciprocal space. We achieve a state-of-the-art measurement sensitivity of $
2.30(8)\times 10^{-26}$ N/$\sqrt{\rm \bf Hz}$. Long-term stabilities on the
order of $10^{-28}$ N are observed in the two spatial components of a force,
which allows probing atomic Van der Waals forces at a millimeter distance
\cite{NatureNanoScanning}. As a further illustrative application, we use our
atomic sensor to calibrate the control precision of an alternating
electromagnetic force applied in the experiment. Future developments of our
method hold promise for delivering unprecedented atom-based quantum force
sensing technologies.
