Creating full-Bloch Bose–Einstein condensates with Ramanq-plates

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.

Quantum measurement arrow of time and fluctuation relations for measuring spin of ultracold atoms

“…We perform weak measurements of spin in a spinor BEC of 87 Rb prepared in a coherent superposition of spin states using optical Raman imprinting techniques (Fig. 1 a and Supplementary Note 1 ) 35 , 36 . We begin by considering the case where the system is initialized to a spatially uniform coherent superposition of spin states to provide evidence for absolute irreversibility in quantum spin measurement 17 .…”

Vectorial light-matter interaction -- exploring spatially structured complex light fields

“…The generation and properties of such vector vortices are the subject of ongoing investigations. [201][202][203][204][205][206][207]…”

SU(2) geometric phase induced by a periodically driven Raman process in ultracold dilute Bose gas

“…In this section we consider strategies for creating the periodic Hamiltonian discussed in the previous section using a Raman process in the ground state manifold of a 87 Rb atom. The Raman process has a variety of applications in the study of ultracold atoms, including quantum state manipulation, generating artificial gauge potentials and spin-orbit coupling, and creating topological defects [24][25][26][27][28][29]. We consider…”

“…1(a). The Raman process is realized by applying two co-propagating circularly polarized lasers to the ultracold atoms, which are subject to a weak bias magnetic field oriented along the beam axis (z-axis) [24,25,28,29]. Since the Raman lasers that we consider couple our pseudo-spin-1/2 states in the 5 2 S 1 2 , F = 1 manifold to the excited states in the 5 2 P 1 2 , F = 1 and F = 2 hyperfine levels, the level diagram that we use in our calculation is actually a W -type instead of Λ-type [24], see Fig.…”