Optical knots in atmospheric turbulence

Topological states of light have recently attracted significant attention in classical and quantum optics due to their predicted topological stability, which is important in applications ranging from classical and quantum communications to imaging and optical manipulation. From the mathematical viewpoint, topological stability implies that one object can be transformed into another by continuous deformation without cutting the lines or allowing them to pass through themselves. While initial studies addressed the robustness of optical knots under phase aberrations, further challenges remain in understanding their stability in realistic turbulent environments. In this talk, we discuss the behavior of optical knots perturbed by atmospheric turbulence and analyze their topological stability over multiple realizations on several turbulence levels. We find that although these structures are relatively stable in the weakly perturbed regime, the number of crossing changes in stronger turbulence conditions. However, we find that the overall three-dimensional singularity shape closely resembles the original one, even in cases where the topology changes.