Mapping out atom-wall interaction with atomic clocks

We explore a feasibility of measuring atom-wall interaction using atomic clocks based on atoms trapped in engineered optical lattices. Optical lattice is normal to the wall. By monitoring the wall-induced clock shift at individual wells of the lattice, one would measure a dependence of the atom-wall interaction on the atom-wall separation. We rigorously evaluate the relevant clock shifts and show that the proposed scheme may uniquely probe the long-range atom-wall interaction in all three qualitatively-distinct regimes of the interaction: van der Waals (image-charge interaction), Casimir-Polder (QED vacuum fluctuations) and Lifshitz (thermal bath fluctuations). The analysis is carried out for atoms Mg, Ca, Sr, Cd, Zn, and Hg, with a particular emphasis on Sr clock.