Atom and photon measurement in cooperative scattering by cold atoms

In this paper, we study cooperative scattering of low intensity light by a cloud of N two-level systems. We include the incident laser field driving these two-level systems and compute the radiation pressure force on the center of mass of the cloud. This signature is of particular interest for experiments with laser cooled atoms. Including the complex coupling between dipoles in a scalar model for dilute clouds of two-level systems, we obtain expression for cooperative scattering forces taking into account the collective Lamb shift. We also derive the expression of the radiation pressure force on a large cloud of two-level systems from an heuristic approach and show that at lowest driving intensities this force is identical for a product and an entangled state.