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Atom optics demonstrates optical phenomena with coherent matter waves,providing a foundational connection between light and matter. Significantadvances in optics have followed the realisation of structured light fieldshosting complex singularities and topologically non-trivial characteristics.However, analogous studies are still in their infancy in the field of atomoptics. Here, we investigate and experimentally create knotted quantumwavefunctions in spinor Bose--Einstein condensates which display non-trivialtopologies. In our work we construct coordinated orbital and spin rotations ofthe atomic wavefunction, engineering a variety of discrete symmetries in thecombined spin and orbital degrees of freedom. The structured wavefunctions thatwe create map to the surface of a torus to form torus knots, M\"obius strips,and a twice-linked Solomon's knot. In this paper we demonstrate strikingconnections between the symmetries and underlying topologies of multicomponentatomic systems and of vector optical fields--a realization of topologicalatom-optics.

Topological atom optics and beyond with knotted quantum wavefunctions