We here demonstrate experimentally how the interplay between the two mechanisms in large systems of quantum emitters leads to spatial variations of photon correlations. The implementation with trapped ion crystals in free space allows us to observe the anticorrelation between photon rates and variance of the photon number distributions in chains of up to 18 ions. For smaller crystals of 4 ions, the transition from antibunching to bunching and super-Poissonian statistics of the scattered light is reported. For higher numbers of scatterers, the photon statistics still display a strong deviation from the fully incoherent scattering case. We also discuss how extraordinary two-photon correlations are obtained in the limit of a weak drive, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. Our results illustrate how the interference of coherent scattering, combined with spontaneous emission, provides a control mechanism for the light statistics.

References
[1] “Coherent Control of Photon Correlations in Trapped Ion Crystals”, K Singh, A Cidrim, A Kovalenko, TM
Pham, O Číp, L Slodička, and R Bachelard, Phys. Rev. Lett. 134, 203602 (2025).[2] “Light Statistics from Large Ensembles of Independent Two-level Emitters: Classical or Non-classical?”
M Bojer, A Cidrim, P P Abrante, R Bachelard, and J von Zanthier, Phys. Rev. A 112, L061701 (2025)