Singular atom optics via stimulated Raman interactions in Spinor Bose–Einstein condensates

Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2016.Many singularities in nature are challenging to study because they are difficult to find or create, thereby making the task of observing their evolution and interactions particularly arduous. Fortunately, we can gain insight into these systems through topological analogy. Sculpting the phase and polarization profiles of optical beams has led to the field of singular optics, in which the morphology of the optical beams with singularities can serve as topological analogs of other physical systems. Ultracold atomic Bose-Einstein condensates are the matter-wave equivalent of optical laser beams. Atoms can have higher dimensional spin manifolds than light and can interact without the mediation of an additional nonlinear medium. By developing an analogy between optical polarization and atomic spin, we can use the mathematical language and techniques of singular optics to both create and study singularities in spinor Bose-Einstein condensates. Just as optical polarization is manipulated with components composed of atoms, atom-optic polarization can manipulated by components composed of light. We use a coherent, stimulated, two-photon Raman interaction as a waveplate for atoms with a retardance given by the pulse area and the waveplate angle set by the relative phase between the beams. The Raman waveplate, along with a Stern–Gerlach state separation technique that serves as an analog of a polarizing beamsplitter, allows us to perform a form of atom-optic polarimetry on the condensate revealing maps of the atomic Stokes parameters. This technique allows us to reconstruct the spinor wavefunction up to a global phase. Using ideas from singular optics, we characterize singularities within the cloud by examining the shape of the local spin precession and maps of the relative phase. When the Raman beams possess spatially varying phase and polarization profiles, they serve as phase plates, or q-plates, for the atoms-they imprint the optical properties, including singularities, into the atomic wavefunction. These techniques will allow us to measure the Gouy phase for matter waves and implement a protocol for single qubit quantum gates. Extending these mathematical foundations to higher dimensions permits studying a richer class of topological structures such as spin monopoles, skyrmions, and both fractional and non-Abelian vortices