  We propose a quantum enhanced interferometric protocol for gravimetry and
force sensing using cold atoms in an optical lattice supported by a
standing-wave cavity. By loading the atoms in partially delocalized
Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities
arising from the mismatch between the lattice and cavity fields and to generate
spin squeezed states via a uniform one-axis twisting model. The quantum
enhanced sensitivity of the states is combined with the subsequent application
of a compound pulse sequence that allows to separate atoms by several lattice
sites. This, together with the capability to load small atomic clouds in the
lattice at micrometric distances from a surface, make our setup ideal for
sensing short-range forces. We show that for arrays of $10^4$ atoms, our
protocol can reduce the required averaging time by a factor of $10$ compared to
unentangled lattice-based interferometers after accounting for primary sources
of decoherence.
