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We study the miscibility properties and ground state phases of two-componentspin-orbit (SO) coupled Bose-Einstein condensates (BECs) in a harmonic trapwith strong axial confinement. By numerically solving the coupledGross-Pitaevskii equations in the two-dimensional setting, we analyze theSO-coupled BECs for two possible permutations of the intra- and interspeciesinteractions, namely (i) weak intra- and weak interspecies interactions (W-W)and (ii) weak intra- and strong interspecies interactions (W-S). Consideringthe density overlap integral as a miscibility order parameter, we investigatethe miscible-immiscible transition by varying the coupling parameters. Weobtain various ground state phases, including plane wave, half quantum vortex,elongated plane wave, and different stripe wave patterns for W-W interactions.For finite Rabi coupling, an increase in SO coupling strength leads to thetransition from the fully miscible to the partially miscible state. We alsocharacterize different ground states in the coupling parameter space using theroot mean square sizes of the condensate. The spin density vector for theground state phases exhibits density, quadrupole and dipole like spinpolarizations. For the W-S interaction, in addition to that observed in the W-Wcase, we witness semi vortex, mixed mode, and shell-like immiscible phases. Wenotice a wide variety of spin polarizations, such as density, dipole,quadrupole, symbiotic, necklace, and stripe-like patterns for the W-S case. Adetailed investigation in the coupling parameter space indicates immiscible tomiscible state phase transition upon varying the Rabi coupling for a fixedRashba SO coupling. The critical Rabi coupling for the immiscible-misciblephase transition decreases upon increasing the SO coupling strength.

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