Creating full-Bloch Bose-Einstein condensates with Raman q-plates

• Published in: Journal of optics (2010) 2016-06, Vol.18 (6), p.64009
• Main Authors: Schultz, Justin T, Hansen, Azure, Murphree, Joseph D, Jayaseelan, Maitreyi, Bigelow, Nicholas P
• Format: Article
• Language: English
• Subjects: atom optics; Bloch sphere; Bose-Einstein condensates; plates; polarization; singular optics; spinor systems
• ISSN: 2040-8978; 2040-8986
• DOI: 10.1088/2040-8978/18/6/064009

A coherent two-photon optical Raman interaction in a pseudo-spin-1/2 Bose-Einstein condensate (BEC) serves as a q-plate for atoms, converting spin to orbital angular momentum. This Raman q-plate has a singular pattern in its polarization distribution in analogy to the singular birefringent q-plates used in singular optics. The vortex winding direction and magnitude as well as the final spin state of the BEC depend on the initial spin state and the topology of the optical Raman q-plate beams. Drawing on the mathematical and geometric foundations of singular optics, we derive the equivalent Jones matrix for this Raman q-plate and use it to create and characterize atomic spin singularities in the BEC that are analogous to optical C-point singularities in polarization. By tuning the optical Raman parameters, we can generate a coreless vortex spin texture which contains every possible superposition in a two-state system. We identify this spin texture as a full-Bloch BEC since every point on the Bloch sphere is represented at some point in the cross section of the atomic cloud. This spin-orbit interaction and the spin textures it generates may allow for the observation of interesting geometric phases in matter waves and lead to schemes for topological quantum computation with spinor BECs.