  We propose an experiment to create and verify entanglement between remote
mechanical objects by use of an optomechanical interferometer. Two optical
cavities, each coupled to a separate mechanical oscillator, are coherently
driven such that the oscillators are laser cooled to the quantum regime. The
entanglement is induced by optical measurement and comes about by combining the
output from the two cavities to erase which-path information. It can be
verified through measurements of degrees of second-order coherence of the
optical output field. The experiment is feasible in the regime of weak
optomechanical coupling. Realistic parameters for the membrane-in-the-middle
geometry suggest entangled state lifetimes on the order of milliseconds.
