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, Möbius 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

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, Möbius 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

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Creating atomic Stokes vortices with spin-1 atomic wave functions

The formal correspondences between pseudo-spin-1/2 systems in optics and in atomic physics have provided fertile ground for exploring polarization in atom optics. Previous experimental results demonstrated atomic polarimetry techniques for two-level wave functions and explored wave-field singularities in the multicomponent wave function of a spinor Bose-Einstein condensate using visualization techniques developed in optics [J. T. Schultz, A. Hansen, and N. P. Bigelow, Opt. Lett. 39, 4271 (2014); A. Hansen, J. T. Schultz, and N. P. Bigelow, Optica 3, 355 (2016)]. Here we further this discussion, reexamining the atomic Stokes parameters and Stokes polarimetry in the context of spin-1 systems where the tensor moments of the higher-spin system enrich the physics considerably. We show that our atomic polarimetry methods provide tools to engineer the multipole tensor moments of the higher-spin atomic wave function, and to realize nontrivial couplings between these multipole moments and an atomic center-of-mass orbital angular momentum. The different forms of coupling between internal tensor moments and external angular momenta can be used to realize a variety of topological structures in the atomic wave field. We identify these - and 2⁢-symmetric features in the streamlines of the atomic Stokes fields constructed in analogy with singular optics

Creating atomic Stokes vortices with spin-1 atomic wave functions

The formal correspondences between pseudo-spin-1/2 systems in optics and in atomic physics have provided fertile ground for exploring polarization in atom optics. Previous experimental results demonstrated atomic polarimetry techniques for two-level wave functions and explored wave-field singularities in the multicomponent wave function of a spinor Bose-Einstein condensate using visualization techniques developed in optics [J. T. Schultz, A. Hansen, and N. P. Bigelow, Opt. Lett. 39, 4271 (2014); A. Hansen, J. T. Schultz, and N. P. Bigelow, Optica 3, 355 (2016)]. Here we further this discussion, reexamining the atomic Stokes parameters and Stokes polarimetry in the context of spin-1 systems where the tensor moments of the higher-spin system enrich the physics considerably. We show that our atomic polarimetry methods provide tools to engineer the multipole tensor moments of the higher-spin atomic wave function, and to realize nontrivial couplings between these multipole moments and an atomic center-of-mass orbital angular momentum. The different forms of coupling between internal tensor moments and external angular momenta can be used to realize a variety of topological structures in the atomic wave field. We identify these - and 2⁢-symmetric features in the streamlines of the atomic Stokes fields constructed in analogy with singular optics

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, Möbius 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