  We study cavity optomechanics of a mixture of ultracold atoms with tunable
nonlinear collisions. We show that atomic collisions provide linear couplings
between fictitious condensate oscillators, leading to possibilities of
achieving a globally coupled quantum optomechanical network with an integrated
atom chip. Potential applications range from simulating collective
nonequilibrium dynamics in fields well past physics to probing unique
properties of quantum mixtures.
