Mathieu–Gauss photons: non-diffraction and self-healing at the quantum regime

Abstract Quantum entanglement represents one of the most fascinating aspects of quantum mechanics and underpins the advancement of next-generation quantum-based technologies. Of particular interest is quantum entanglement in the spatial degree of freedom of light. As such, in this paper, we analyze a two-photon orbital angular momentum entangled state, decomposed in terms of helical Mathieu–Gauss ( HMG ) modes and generated through a type II spontaneous parametric down conversion process. Furthermore, a spatially-resolved heralded single photon detection system allowed the observation of the transverse spatial distribution of correlated HMG photons and the corroboration of their self-healing and non-diffractive properties. More precisely, we were able to corroborate that HMG photons maintain the same non-diffractive properties of classical HMG beams and that their time-averaged transverse field distribution reconstructs itself upon propagation in the presence of an opaque obstacle.