Collective generation of quantum states of light by entangled atoms

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.