Atom and nanoparticle arrays trapped in optical lattices are shown to be
capable of sustaining collective oscillations of frequency proportional to the
strength of the external light field. The spectrum of these oscillations
determines the mechanical stability of the arrays. This phenomenon is studied
for dimers, strings, and two-dimensional planar arrays. Laterally confined
particles free to move along an optical channel are also considered as an
example of collective motion in partially-confined systems. The fundamental
concepts of dynamical response in optical matter introduced here constitute the
basis for potential applications to quantum information technology and signal
processing. Experimental realizations of these systems are proposed.Comment: 4 figures. Optics Express (in press