  We propose an experiment utilizing an array of cooled micro-cantilevers
coupled to a sample of ultra-cold atoms trapped near a micro-fabricated
surface. The cantilevers allow individual lattice site addressing for atomic
state control and readout, and potentially may be useful in optical lattice
quantum computation schemes. Assuming resonators can be cooled to their
vibrational ground state, the implementation of a two-qubit controlled-NOT gate
with atomic internal states and the motional states of the resonator is
described. We also consider a protocol for entangling two or more cantilevers
on the atom chip with different resonance frequencies, using the trapped atoms
as an intermediary. Although similar experiments could be carried out with
magnetic microchip traps, the optical confinement scheme we consider may
exhibit reduced near-field magnetic noise and decoherence. Prospects for using
this novel system for tests of quantum mechanics at macroscopic scales or
quantum information processing are discussed.
