revised and extended version ; International audience ; 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~$μ$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 $≈ 10^{-4}$~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 $≥$~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~$μ$m.