  In this article we discuss and compare different ways to engineer an
interface between ultracold atoms and micro- and nanomechanical oscillators. We
start by analyzing a direct mechanical coupling of a single atom or ion to a
mechanical oscillator and show that the very different masses of the two
systems place a limit on the achievable coupling constant in this scheme. We
then discuss several promising strategies for enhancing the coupling:
collective enhancement by using a large number of atoms in an optical lattice
in free space, coupling schemes based on high-finesse optical cavities, and
coupling to atomic internal states. Throughout the manuscript we discuss both
theoretical proposals and first experimental implementations.
