  We consider a quantum optomechanical scheme wherein an ordered
two-dimensional array of laser-trapped atoms is used as a movable membrane. The
extremely light mass of the atoms yields very strong optomechanical coupling,
while their spatial order largely eliminates scattering losses. We show that
this combination opens the way for quantum optomechanical nonlinearities, well
within the ultimate single-photon strong-coupling regime. As an example, we
analyze the possibility to observe optomechanically induced quantum effects
such as photon blockade and time-delayed non-classical correlations. We discuss
novel opportunities opened by the optomechanical backaction on the internal
states of the array atoms.
