Nonlinear optics in 2D materials: from classical to quantum

Nonlinear optics has long been a cornerstone of modern photonic technology, enabling a wide array of applications, from frequency conversion to the generation of ultrafast light pulses. Recent breakthroughs in two-dimensional (2D) materials have opened a frontier in this field, offering new opportunities for both classical and quantum nonlinear optics. These atomically thin materials exhibit strong light-matter interactions and large nonlinear responses, thanks to their tunable lattice symmetries, strong resonance effects, and highly engineerable band structures. In this paper, we explore the potential that 2D materials bring to nonlinear optics, covering topics from classical nonlinear optics to nonlinearities at the few-photon level. We delve into how these materials enable possibilities, such as symmetry control, phase matching, and integration into photonic circuits. The fusion of 2D materials with nonlinear optics provides insights into the fundamental behaviors of elementary excitations such as electrons, excitons, and photons in low dimensional systems and has the potential to transform the landscape of next-generation photonic and quantum technologies.