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Light propagation in disordered media is a fundamental and important problemin optics and photonics. In particular, engineering light-matter interaction indisordered cold atomic ensembles is one of the central topics in modern quantumand atomic optics. The collective response of dense atomic gases under lightexcitation, which crucially depends on the spatial distribution of atoms andthe geometry of the ensemble, has important impacts on quantum technologieslike quantum sensors, atomic clocks and quantum information storage. Here weanalyze near-resonant light transmission in two-dimensional dense ultracoldatomic ensembles with short-range positional correlations. Based on thecoupled-dipole simulations under different atom number densities andcorrelation lengths, we show that the collective effects are stronglyinfluenced by those positional correlations, manifested as significant shiftsand broadening or narrowing of transmission resonance lines. The results showthat mean-field theories like Lorentz-Lorenz relation are not capable ofdescribing such collective effects. We further investigate the statisticaldistribution of eigenstates, which are significantly affected by the interplaybetween dipole-dipole interactions and position correlations. This work canprovide profound implications on collective and cooperative effects in coldatomic ensembles as well as the study of mesoscopic physics concerning lighttransport in strongly scattering disordered media.

Near-resonant light transmission in two-dimensional dense cold atomic media with short-range positional correlations