Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate

We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin-1/2 system. The spin state of a spin-1/2 quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases, and the relative frequencies. We experimentally demonstrate key features of this model with a $^{87}$Rb spinor Bose-Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.Comment: 13 pages, 13 figures, submitted to the Journal of Modern Optics "20 Years of Bose-Einstein condensates" Special Issu

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

Hay Press.

Patent for an improved, inexpensive, and simple hay press that "alternately feed[s] the hay into the chamber, and press the same, the two mechanisms being operated from the same source; to provide for increase of power, and for regulating the tension or mouth of the press at the point of exit of the completed bale" (lines 12-18)

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