Emission photon statistics in collectively interacting dipole atom arrays in the low-intensity limit

We investigate the photon statistics of light emitted from a system of collectively interacting dipoles in the low-intensity regime, incorporating double-excitation states to capture beyond-single-excitation effects. By analyzing the eigenstates of the double-excitation manifold, we establish their connection to the accessible single-excitation eigenmodes and investigate the role of decay rates in shaping the zero-time-delay photon correlation function $g^{(2)}(\tau = 0)$ under different detection schemes. The photon emission statistics can be arbitrarily controlled by interfering two beams of light that selectively address orthogonal eigenmodes. This can act as a tunable nonlinearity that enables both enhancement or suppression of two-photon emission.