  We present a theoretical framework to describe the collective emission of
light by entangled atomic states. Our theory applies to the low excitation
regime, where most of the atoms are initially in the ground state, and relies
on a bosonic description of the atomic excitations. In this way, the problem of
light emission by an ensemble of atoms can be solved exactly, including
dipole-dipole interactions and multiple light scattering. Explicit expressions
for the emitted photonic states are obtained in several situations, such as
those of atoms in regular lattices and atomic vapors. We determine the
directionality of the photonic beam, the purity of the photonic state, and the
renormalization of the emission rates. We also show how to observe collective
phenomena with ultracold atoms in optical lattices, and how to use these ideas
to generate photonic states that are useful in the context of quantum
information.
