Topological atom optics and beyond with knotted quantum wavefunctions

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realization of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose-Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, Mobius strips, and a twice-linked Solomon's knot. In this paper we demonstrate close connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields-a realization of topological atom-optics. Knots are mathematically and physically complex objects that have only rarely been realized in quantum fluids and optics. The authors create knotted quantum wavefunctions of a spinor Bose gas and recognize a close mapping of the results to a recent realization of knots in the polarization of an optical field, exploring common features of topology: a topological atom optics.