Grating Lobes in Higher-Order Correlation Functions of Arrays of Quantum Emitters: Directional Photon Bunching Versus Correlated Directions

Recent advances in nanofabrication and optical manipulation techniques are making it possible to build arrays of quantum emitters with accurate control over the locations of their individual elements. In analogy with classical antenna arrays, this poses new opportunities for tailoring quantum interference effects by designing the geometry of the array. Here, we investigate the N th -order directional correlation function of the photons emitted by an array of N initially-excited identical quantum emitters, addressing the impact of the appearance of grating lobes. Our analysis reveals that the absence of directivity in the first-order correlation function is contrasted by an enhanced directivity in the N th -order one. This suggests that the emitted light consists of a superposition of directionally entangled photon bunches. Moreover, the photon correlation landscape changes radically with the appearance of grating lobes. In fact, the photons no longer tend to be bunched along the same direction; rather, they are distributed in a set of correlated directions with equal probability. These results clarify basic aspects of light emission from ensembles of quantum emitters. Furthermore, they may find applications in the design of nonclassical light sources.

SOME DIRECTIONAL CORRELATION FUNCTIONS FOR SUCCESSIVE NUCLEAR RADIATIONS

A method of evaluating the sums of angular momentum coefficients appearing in the directional correlation function for successive nuclear radiations is presented. The sums are evaluated for the simplest cases and alpha–gamma and gamma–gamma correlation functions are calculated for these cases—the angular momentum quantum number of one of the emitted particles being arbitrary and that of the other being 1 or 2.