Stability of optical knots in atmospheric turbulence

Topology advances the understanding of many branches of science and technology, from elementary particle physics to condensed matter physics. While the topological stability of mathematical knots implies robustness to perturbations and suggests their potential as information carriers, the behavior of optical knots in perturbative environments is largely unexplored. Here, we experimentally and theoretically investigate the effects of atmospheric turbulence on optical knot stability and demonstrate that their topological invariant can be preserved in the weak turbulence regime but may not be conserved in the stronger turbulence conditions, despite their topological nature. Such topology transitions occur through reconnection events, where the additional optical modes resulting from the interactions with the turbulent medium change the vortex lines in space. Additionally, we propose an optimization algorithm to maximize the distance between the phase singularities at each longitudinal plane, facilitating measurements of optical knots and improving their performance in the presence of turbulence.