Vortex knots in a Bose-Einstein condensate

We present a method for numerically building a vortex knot state in the superfluid wave function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and shape preservation of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how vortex knots break up into vortex rings.