Influence of Rashba spin–orbit and Rabi couplings on the spin-mixing and ground state phases of binary Bose–Einstein condensates

We study the miscibility properties and ground state phases of two-component spin-orbit (SO) coupled Bose-Einstein condensates (BECs) in a harmonic trap with strong axial confinement. By numerically solving Gross-Pitaevskii equations two-dimensional setting, we analyze SO-coupled BECs for two possible permutations intra- interspecies interactions, namely (i) weak interactions (W-W) (ii) (W-S). Considering density overlap integral as order parameter, investigate miscible-immiscible transition by varying coupling parameters. obtain various phases, including plane wave, half quantum vortex, elongated different stripe wave patterns W-W interactions. For finite Rabi coupling, an increase SO strength leads to from fully miscible partially state. also characterize states parameter space using root mean square sizes condensate. The spin vector exhibits density, quadrupole dipole like polarizations. W-S interaction, addition that observed case, witness semi mixed mode, shell-like immiscible phases. notice wide variety polarizations, such dipole, quadrupole, symbiotic, necklace, stripe-like case. A detailed investigation indicates phase upon fixed Rashba coupling. critical immiscible-miscible decreases increasing strength.