We investigate the phase transition of the Bose-Einstein condensates with equal-weight Rashba and Dresselhaus spin-orbit coupling trapped in one-dimensional optical lattice. Based on the variational and two-mode approximation, the critical condition for phase transition between polarized and unpolarized Bloch wave phase is obtained analytically for the first time, which explicitly reveals rich competitive relationship among spin-orbit coupling, optical lattice and atomic interactions in determining the phase transition of the system. It is shown that the change of the energy minima and the phase transition point by the optical lattice depends on the atomic interactions and spin-orbit coupling. Our results provide a theoretical evidence for deep understanding of the competition mechanism between the optical lattice and spin-orbit coupling for the ground state phase transition of spin-orbit-coupled Bose-Einstein condensates in optical lattice.

我们研究了一维光学晶格中具有等重Rashba和Dresselhaus自旋轨道耦合的Bose-Einstein凝聚物的相变。在变分和双模近似的基础上，首次解析获得了极化和非极化布洛赫波相位之间相变的临界条件，从而明确揭示了自旋轨道耦合，光学晶格和原子相互作用之间的丰富竞争关系。系统的相变。结果表明，光学晶格对能量极小值和相变点的改变取决于原子的相互作用和自旋轨道耦合。