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We present a theoretical framework to describe the collective emission oflight by entangled atomic states. Our theory applies to the low excitationregime, where most of the atoms are initially in the ground state, and relieson a bosonic description of the atomic excitations. In this way, the problem oflight emission by an ensemble of atoms can be solved exactly, includingdipole-dipole interactions and multiple light scattering. Explicit expressionsfor the emitted photonic states are obtained in several situations, such asthose of atoms in regular lattices and atomic vapors. We determine thedirectionality of the photonic beam, the purity of the photonic state, and therenormalization of the emission rates. We also show how to observe collectivephenomena with ultracold atoms in optical lattices, and how to use these ideasto generate photonic states that are useful in the context of quantuminformation.

Collective generation of quantum states of light by entangled atoms