University of David
The idea of knotted fields has gained renewed interest recently23,24, as the role of topology comes to the forefront in a range of physical systems, from knot invariants in statistical mechanics25, to topological insulators in condensed matter26, and quantum computing27. Crucially, experimental techniques are now at a stage where knotted and linked topological defect filaments can be engineered in liquid crystals11,17 and laser light28–31. In the latter case, similar to a one-component BEC22, the field consists of a complex scalar amplitude, in which the defects are quantized vortices32,33 — circulations of energy flow where the intensity is zero and the phase undefined34,35. A variety of knotted and linked optical vortices can be synthesized with tailored superpositions of free-space modes28,31, successfully implemented in experiments with Gaussian laser beams controlled by holograms29–31. However, knot topology appears rare if these superpositions are not chosen carefully36,37.Asimilar approach to the construction of knotted optical fields28,31 was employed for vortex knots in BECs22. The striking difference, however, is that vortex knots in BECs undergo essentially nonlinear temporal dynamics due to atomatom interactions, whereas optical vortex knots occur as a result of linear interference and are static in time29–31. Knots in BECs with repulsive interatomic interaction disintegrate via series of vortex reconnections22.