  The collective emission from a one-dimensional chain of interacting two-level
atoms coupled to a common electromagnetic reservoir is investigated. We derive
the system's dissipative few-excitation eigenstates, and analyze their static
properties, including the collective dipole moments and branching ratios
between different eigenstates. Next, we study the dynamics, and characterize
the light emitted or scattered by such a system via different far-field
observables. Throughout the analysis, we consider spontaneous emission from an
excited state as well as two different pump field setups, and contrast the two
extreme cases of non-interacting and strongly interacting atoms. For the latter
case, the two-excitation submanifold contains a two-body bound state, and we
find that the two cases lead to different dynamics and far-field signatures.
Finally we exploit these signatures to characterize the wavefunctions of the
collective eigenstates. For this, we identify a direct relation between the
collective branching ratio and the momentum distribution of the collective
eigenstates' wavefunction. This provides a method to proof the existence of
certain collective eigenstates and to access their wave function without the
need to individually address and/or manipulate single atoms.

Quantum Physics;Atomic Physics