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 o
ptically 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.
We consider a small partially reflecting vibrating mirror coupled dispersively to a single optical mode of a high finesse cavity. We show this arrangement can be used to implement quantum squeezing of the mechanically oscillating mirror.
