  We discuss theoretically the optical binding of one-dimensional chains of
cold atoms shone by a transverse pump, where particles self-organize to a
distance close to an optical wavelength. As the number of particles is
increased, the trapping potential increases logarithmically as the
contributions from all atoms add up constructively. We identify a cooperative
cooling mechanism, due to the mutual exchange of photons between atoms, which
can beat the spontaneous emission for chains that are long enough.
Surprisingly, the cooling is optimal very close to the resonance. This peculiar
cooling mechanism thus gives new insights into the cooperative physics of
low-dimensional cold atom systems.
