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Tailored long range forces on polarizable particles by collective scattering of broadband radiation

Collective coherent light scattering by polarizable particles creates surprisingly strong, long range inter-particle forces originating from interference of the light scattered by different particles. While for monochromatic laser beams this interaction decays with the inverse distance, we show here that in general the effective interaction range and geometry can be controlled by the illumination bandwidth and geometry. As generic example we study the modifications inter-particle forces within a 1D chain of atoms trapped in the field of a confined optical nanofiber mode. For two particles we find short range attraction as well as optical binding at multiple distances. The range of stable distances shrinks with increasing light bandwidth and for a very large bandwidth field as e.g. blackbody radiation we find a strongly attractive potential up to a critical distance beyond which the force gets repulsive. Including multiple scattering can even lead to the appearance of a stable configuration at a large distance. Such broadband scattering forces should be observable contributions in ultra-cold atom interferometers or atomic clocks setups. They could be studied in detail in 1D~geometries with ultra-cold atoms trapped along or within an optical nanofiber. Broadband radiation force interactions might also contribute in astrophysical scenarios as illuminated cold dust clouds.