Nonlinear effects in Anderson localization of light by two-level atoms

We investigate the simultaneous presence of several photons in disordered three-dimensional cold atom clouds, beyond the idealized condition of a single photon for Anderson localization. We find that the presence of these multiple excitations does not affect substantially the abnormal intensity fluctuations which characterize the Anderson localization transition, provided that the radiated light is frequency filtered. Indeed, long-lived modes, and particularly the localized ones, are strongly saturated even for a weak pump, leading to a large increase of the inelastic scattering and to reduced fluctuations in the total radiation. Yet the atomic coherences and the resulting elastic scattering remain a proper witness of the Anderson localization transition. Thus, frequency filtering appears as an efficient tool to discriminate single-excitation phenomena from many-body ones, and one can expect that the fluorescence spectrum will in turn allow us to investigate many-body localization.