Raman-induced spin-orbit-coupled and spin-tensor-momentum-coupled spin-1 Bose-Einstein condensates in a toroidal trap

Abstract

In a spin-1 spinor BEC, spin-orbit coupling or spin-tensor-momentum coupling can be experimentally implemented by Raman lasers induced transitions. We study ground states of a spin-1 BEC with these two experimentally realizable Raman-induced couplings in the presence of a toroidal trap. The similarity and difference of ground states between these two couplings are addressed. The spin-flip symmetries and the toroidal trap together make the density of ground states feature two lobes. The effect of quadratic Zeeman shift and the detuning on ground states is discussed based on the single-particle dispersion relation.