  Light-matter interacting quantum systems manifest strong correlations that
lead to distinct cooperative spontaneous emissions of subradiance or
superradiance. To demonstrate the essence of long-range correlations in such
systems, we consider an atomic array under the resonant dipole-dipole
interactions (RDDI) and apply an interpretable machine learning with the
integrated gradients to identify the crossover between the subradiant and
superradiant sectors. The machine shows that the next nearest-neighbor
couplings in RDDI play as much as the roles of nearest-neighbor ones in
determining the whole eigenspectrum within the training sets. Our results
present the advantage of machine learning approach with explainable ability to
reveal the underlying mechanism of correlations in quantum optical systems,
which can be potentially applied to investigate many other strongly interacting
quantum many-body systems.
