  We describe a novel experiment based on atoms trapped close to a macroscopic
surface, to study the interactions between the atoms and the surface at very
small separations (0.6 to 10 $\mu$m). In this range the dominant potential is
the QED interaction (Casimir-Polder and Van der Waals) between the surface and
the atom. Additionally, several theoretical models suggest the possibility of
Yukawa type potentials with sub-mm range, arising from new physics related to
gravity. The proposes set-up is very similar to neutral atom optical lattice
clocks, but with the atoms trapped in lattice sites close to the reflecting
mirror. A sequence of pulses of the probe laser at different frequencies is
then used to create an interferometer with a coherent superposition between
atomic states at different distances from the mirror (in different lattice
sites). Assuming atom interferometry state of the art measurement of the phase
difference and a duration of the superposition of about 0.1 s we expect to be
able to measure the potential difference between separated states with an
uncertainty of $\approx 10^{-4}$ Hz. An analysis of systematic effects for
different atoms and surfaces indicates no fundamentally limiting effect at the
same level of uncertainty, but does influence the choice of atom and surface
material. Based on those estimates, we expect that such an experiment would
improve the best existing measurements of the atom-wall QED interaction by
$\geq$ 2 orders of magnitude, whilst gaining up to 4 orders of magnitude on the
best present limits on new interactions in the range between 100 nm and 100
$\mu$m.
