Probing few-excitation eigenstates of interacting atoms on a lattice by observing their collective light emission in the far field

The collective emission from a one-dimensional chain of interacting two-level atoms coupled to a common electromagnetic reservoir is investigated. We derive the systems 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.