The paper discusses the creation and study of spin-orbit (SO) coupling in a neutral atomic Bose-Einstein condensate (BEC) using a pair of Raman lasers. This is the first realization of SO coupling in ultracold atomic gases and for bosons. The SO coupling, which is equivalent to that of an electronic system with equal Rashba and Dresselhaus couplings, modifies the interactions between two dressed atomic spin states, leading to a quantum phase transition from a spatially mixed state to a phase-separated state. The transition is quantitatively agreed with theoretical predictions and demonstrates the potential for realizing topological insulators in fermionic neutral atom systems. The authors also explore the effects of magnetic fields and detunings on the phase diagram, showing that the miscibility condition for a two-component BEC is independent of the number of atoms. The results highlight the practicality of this method for tuning spinor BECs, particularly for fermionic atoms with smaller fine-structure splittings.The paper discusses the creation and study of spin-orbit (SO) coupling in a neutral atomic Bose-Einstein condensate (BEC) using a pair of Raman lasers. This is the first realization of SO coupling in ultracold atomic gases and for bosons. The SO coupling, which is equivalent to that of an electronic system with equal Rashba and Dresselhaus couplings, modifies the interactions between two dressed atomic spin states, leading to a quantum phase transition from a spatially mixed state to a phase-separated state. The transition is quantitatively agreed with theoretical predictions and demonstrates the potential for realizing topological insulators in fermionic neutral atom systems. The authors also explore the effects of magnetic fields and detunings on the phase diagram, showing that the miscibility condition for a two-component BEC is independent of the number of atoms. The results highlight the practicality of this method for tuning spinor BECs, particularly for fermionic atoms with smaller fine-structure splittings.