Title: Population of collective modes in light scattering by many atoms,
Abstract: The interaction of light with an atomic sample containing a large number of
particles gives rise to many collective (or cooperative) effects, such as
multiple scattering, superradiance and subradiance, even if the atomic density
is low and the incident optical intensity weak (linear optics regime). Tracing
over the degrees of freedom of the light field, the system can be well
described by an effective atomic Hamiltonian, which contains the light-mediated
dipole-dipole interaction between atoms. This long-range interaction is at the
origin of the various collective effects, or of collective excitation modes of
the system. Even though an analysis of the eigenvalues and eigenfunctions of
these collective modes does allow distinguishing superradiant modes, for
instance, from other collective modes, this is not sufficient to understand the
dynamics of a driven system, as not all collective modes are significantly
populated. Here, we study how the excitation parameters, i.e. the driving
field, determines the population of the collective modes. We investigate in
particular the role of the laser detuning from the atomic transition, and
demonstrate a simple relation between the detuning and the steady-state
population of the modes. This relation allows understanding several properties
of cooperative scattering, such as why superradiance and subradiance become
independent of the detuning at large enough detuning without vanishing, and why
superradiance, but not subradiance, is suppressed near resonance.