Anisotropic Bose condensate using Bloch state: spin texture and optical effect

Chao Kong, Zheng-Hua Tang, Ning Lu +6 more

Hiroshi Kuratsuji

Azure Hansen, Justin T. Schultz, N. P. Bigelow

Shu-Wei, Song, Lin - +5 more

Justin T. Schultz, Azure Hansen, Joseph D. Murphree +2 more

Abstract 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.

Yue-Xin Huang, Wei Zhuang, Xiang-Fa Zhou +3 more

We report on the Bose-Einstein condensate in the Bloch bands with off-diagonal periodic potential (ODPP), which simultaneously plays the role of spin-orbit coupling and Zeeman field. This model can be realized using two independent Raman couplings in the same three-level system, in which the time-reversal symmetry ensures the energy degeneracy between the two states with opposite momenta. We find that these two Raman couplings can be used to tune the spin polarization in momentum space, thus greatly modifying the effective scatterings over the Bloch bands. We observe a transition from the Bloch plane wave phase with condensate at one wave vector to the Bloch stripe phase with condensate at the two Bloch states with opposite wave vectors. These two phases will exhibit different spin textures and density modulations in real space, which are totally different from that in free space. In momentum space, multiple peaks differing by some reciprocal lattice vectors can be observed in both phases, reflecting the periodic structure of the ODPP. A three-band effective model is proposed to understand these observations. This ODPP will never approach the tight-binding limit, thus can provide an alternative platform in the investigations of various physics, such as collective excitations, polaron, and topological superlfuids, over the Bloch bands.