  We theoretically study the coupling of Bose-Einstein condensed atoms to the
mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is
an experimentally viable hybrid quantum system which allows one to explore the
interface of quantum optics and condensed matter physics. We propose an
experiment where easily detectable atomic spin-flips are induced by the
cantilever motion. This can be used to probe thermal oscillations of the
cantilever with the atoms. At low cantilever temperatures, as realized in
recent experiments, the backaction of the atoms onto the cantilever is
significant and the system represents a mechanical analog of cavity quantum
electrodynamics. With high but realistic cantilever quality factors, the strong
coupling regime can be reached, either with single atoms or collectively with
Bose-Einstein condensates. We discuss an implementation on an atom chip.
