  We investigate theoretically the extension of cavity optomechanics to
multiple membrane systems. We describe such a system in terms of the coupling
of the collective normal modes of the membrane array to the light fields. We
show these modes can be optically addressed individually and be cooled, trapped
and characterized, e.g. via quantum nondemolition measurements. Analogies
between this system and a linear chain of trapped ions or dipolar molecules
imply the possibility of related applications in the quantum regime.
