  We study the energy spectrum of atoms trapped in a vertical 1D optical
lattice in close proximity to a reflective surface. We propose an effective
model to describe the interaction between the atoms and the surface at any
distance. Our model includes the long-range Casimir-Polder potential together
with a short-range Lennard-Jones potential, which are considered
non-perturbatively with respect to the optical lattice potential. We find an
intricate energy spectrum which contains a pair of loosely-bound states
localized close to the surface in addition to a surface-modified Wannier-Stark
ladder at long distances. Atomic interferometry involving those loosely-bound
atom-surface states is proposed to probe the adsorption dynamics of atoms on
mirrors.
