  We investigate the modifications of the frequency-comb-induced radiation
pressure force on cold $^{87}$Rb atoms that are induced by the collective
effects. Collective effects include both coherent and incoherent contributions
and depend on the optical thickness of the atomic cloud. We observe reduction
and broadening of the comb-induced force when the cloud's optical thickness
increases, and compare the measured results with predictions of a coherent
model based on the timed Dicke state approach and an incoherent scattering
model based on the shadow effect explained by Beer-Lambert law. Both models
describe the experimental results well, indicating that an incoherent
scattering approach is sufficient to explain the observed modifications of the
comb-induced force even for larger optical thicknesses. The results support the
analogy between the frequency comb and continuous-wave laser-atom interaction
and thus pave the way toward novel frequency comb applications in laser
cooling, quantum communication, and light-atom interfaces based on structured
and disordered atomic systems.
