Nonlinear optical processes are at the foundation of many applications in modern science and engineering. The emerging field of Quantum Technologies is now demanding that we push these processes into the realm of Quantum Nonlinear Optics (QNLO) where nonlinear effects occur at the level of individual photons. Achieving such a regime would allow the generation and manipulation of non-classical states of light and would open exciting new scenarios involving quantum many-body physics of light. Despite the great efforts that have been invested along this line of research, significant improvements are still necessary to fully achieve the QNLO regime. QUANLUX aims to tackle this challenge by proposing a novel light-matter interface consisting of ordered atomic arrays as an ideal platform to implement QNLO processes. The ultimate objectives consist in identifying new strategies for QNLO protocols that can possibly surpass previously established performance bounds as well as investigating the complex emergent behaviour of strongly interacting photons. To tackle and solve these demanding problems the fellow will make use of advanced numerical and theoretical techniques developed in condensed matter and many-body physics (e.g. tensor networks and diagrammatic approaches) that will be acquired through dedicated training visits to experts in the field. The proposed dissemination and outreach program will progressively spread the outcome of the action to the scientific community and to the general public reinforcing the impact of the research’s results. The originality and multidisciplinary nature of the proposal have the potential to revolutionize the major paradigms currently used to implement QNLO processes and drive a technological innovation in the construction of light-matter interfaces. The action will be conducted by Giuseppe Calajò who will join the Theoretical Quantum Nanophotonics group lead by Prof. Darrick Chang at ICFO, Spain.