Light Induced Inverse-Square Law Interactions between Nanoparticles: "Mock Gravity" at the Nanoscale

The interaction forces between identical resonant molecules or nanoparticles, optically induced by a quasimonochromatic isotropic random light field, are theoretically analyzed. In general, the interaction force exhibits a far-field oscillatory behavior at separation distances larger than the light wavelength. However, we show that the oscillations disappear when the frequency of the random field is tuned to an absorption Fröhlich resonance, at which the real part of the particle's electric polarizability is zero. At the resonant condition, the interaction forces follow a long-range gravitylike inverse square distance law which holds for both near- and far-field separation distances.