We solve self-consistently the coupled equations of motion for trapped
particles and the field of a one-dimensional optical lattice. Optomechanical
coupling creates long-range interaction between the particles, whose nature
depends crucially on the relative power of the pump beams. For asymmetric
pumping, traveling density wave-like collective oscillations arise in the
lattice, even in the overdamped limit. Increasing the lattice size or pump
asymmetry these waves can destabilize the lattice.Comment: 5 pages, minor changes (SI units, new references