  We study the ultimate bounds on the sensitivity of a Bloch-oscillation atom
interferometer where the external force is estimated from the measurement of
the on-site atomic density. For external forces such that the energy difference
between lattice sites is smaller than the tunneling energy, the atomic
wave-function spreads over many lattice sites, increasing the separation
between the occupied modes of the lattice and naturally enhancing the
sensitivity of the interferometer. To investigate the applicability of this
scheme we estimate the effect of uncontrolled fluctuations of the tunneling
energy and the finite resolution of the atom detection. Our analysis shows that
a horizontal lattice combined with a weak external force allow for high
sensitivities. Therefore, this setup is a promising solution for compact
devices or for measurements with high spatial resolution.
