Quantum Knots that Never Come Untied

Lord Kelvin proposed that atoms form hydrodynamic vortex knots. However, they typically untie through reconnections, i. e., local cut-and-slice events, unlike stable vortex unknots such as smoke rings. The same holds in superfluids--quantum fluids with zero viscosity--where vortices have quantized circulation, making them topologically stable. For over 150 years, hydrodynamically stable vortex knots have been sought both experimentally and theoretically. Here, we present the first demonstration of hydrodynamically stable vortex knots and links in experimentally realizable Bose-Einstein condensates of ultracold atomic gases and confirm it through dynamic simulations. Our method creates stable knotted vortex structures in systems where reconnections are prohibited, with potential relevance to neutron star interiors. Additionally, we anticipate our mathematical framework could have applications in quantum computation, quantum turbulence, and DNA dynamics, particularly where reconnections are restricted.