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We consider a two-component pancake-shaped, i.e., effectively two-dimensional(2D), Bose-Einstein condensate (BEC) coupled by the spin-orbit (SO) and Rabiterms. The SO coupling adopted here is of the mixed Rashba-Dresselhaus type.For this configuration, we derive a system of two 2D nonpolynomialSchr\"odinger equations (NPSEs), for both attractive and repulsive interatomicinteractions. In the low- and high-density limits, the system amounts topreviously known models, namely, the usual 2D Gross-Pitaevskii equation, or theSchr\"odinger equation with the nonlinearity of power 7/3. We present simpleapproximate localized solutions, obtained by treating the SO and Rabi terms asperturbations. Localized solutions of the full NPSE system are obtained in anumerical form. Remarkably, in the case of the attractive nonlinearity actingin free space (i.e., without any 2D trapping potential), we find parameterregions where the SO and Rabi couplings make 2D fundamental solitonsdynamically stable.

Localized modes in quasi-2D Bose-Einstein condensates with spin-orbit and Rabi couplings