Phase separation in a spin-orbit-coupled Bose-Einstein condensate

We study a spin-orbit (SO)-coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For an SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any nonzero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like Rb-87. On the other hand, SO coupling favors miscibility in a polar BEC, like Na-23. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided that the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar.