Geometric antibunching and directional shaping of photon anticorrelations

We investigate the directional characteristics of photon statistics in dimers of quantum emitters. For their analysis, we construct a two-point second-order correlation function that allows us to find an alternative mechanism for photon anticorrelation, termed as geometric antibunching. This phenomenon is completely agnostic to the quantum state of the emitters and emerges from quantum interference effects due to the indistinguishability of different two-photon optical pathways. Finally, we explore its occurrence in emitters placed in the vicinity of a flat substrate and a nanosphere, demonstrating its tunability through the different material and geometric parameters of these devices.