Spin-orbit-angular-momentum coupling in a spin-1 Bose-Einstein condensate

We propose a simple model with spin and orbit angular momentum coupling in a spin-1 Bose- Einstein condensate, where three internal atomic states are Raman coupled by a pair of co- propagating Laguerre-Gaussian beams. The resulting Raman transition imposes a transfer of orbital angular momentum between photons and the condensate in a spin-dependent way. Focusing on a regime where the single-particle ground state is nearly three-fold degenerate, we show that the weak interatomic interaction in the condensate produces a rich phase diagram, and that a many-body Rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic Zeeman shift. We carried out our calculations using both a variational method and a full numerical method, and found excellent agreement.