Atom and photon measurement in cooperative scattering by cold atoms

Abstract

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.Comment: 11 pages, 4 figures, article for special issue of PQE 201

Collective effects in the radiation pressure force

“…In Secs. III A-III D, we describe the contributions on the RPF of, resp., diffuse scattering, diffraction, coherent back-scattering and the prediction based on the driven 'timed-Dicke state' [17,36,37]. Finally, we draw our conclusions in Sec.…”

“…It is then convenient to approximate the cloud by a continuous distribution, yet keeping a disorder contribution to recover the single atom limit [30,37]. Then for large clouds, kR ≫ 1, these factors read:…”

“…We use the Coupled-Dipole Equations (CDE) that describe the all-to-all coupling between the atoms, and the scattering events of any order [36,37,41,53,54]. We consider N two-level atomic dipoles with a dimensionless amplitude β j , at positions r j , coupled to an incident laser of field E 0 (r) and wavenumber k close to the atomic transition (linewidth Γ), but also coupled to each other through their radiation field:…”

Cooperativity in light scattering by cold atoms

“…The previous works studying cooperative scattering by weakly excited atoms were based on a effective Hamiltonian model and brought us to a description equivalent to that of N classical linear dipoles driven by the external field [10,13]. Here, we go beyond the linear optics approximation using a master equation approach, still restricted to a single excitation.…”

“…In these works, the authors describe the collective atomic response under continuous excitation of a low intensity light field using an effective Hamiltonian model valid in the linear regime. From it, the average radiation pressure force and the scattered intensity have been derived, observing the modification from the single-atom values due to cooperativity [13]. In this paper, we present an extended model based on a master equation in the single-excitation approximation.…”