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

Abstract: 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 initial-time photon correlation function $g^{(2)}(\tau = 0)$ under different detection schemes. By interfering two beams of light that selectively address orthogonal eigenmodes, the photon emission statistics can be arbitrarily controlled. This can act as a tunable nonlinearity that enables both the enhancement and suppression of photon correlations, extending the operational intensity range for single-photon applications.