光晶格中自旋轨道耦合玻色-爱因斯坦凝聚体的非线性能谱特性

Nonlinear energy band structure of spin-orbit coupled Bose-Einstein condensates in optical lattice

通过两模近似和变分法,研究了光晶格中自旋轨道耦合玻色-爱因斯坦凝聚体的非线性能谱结构和流密度.研究发现,当系统参数满足一定条件时,能谱结构在布里渊区的边界处会出现loop结构,其中光晶格和拉曼耦合会抑制loop结构的出现,而自旋轨道耦合和原子间相互作用会促进loop结构的产生,并使能带结构变得更加复杂.此外,能带结构的变化与凝聚体的流密度密切相关,自旋轨道耦合会使不同自旋态的流密度在动量空间的分布呈现强烈的不对称性并发生分离,而光晶格和拉曼耦合会减弱这种不对称性,使不同自旋态的流密度重合.loop结构破坏了系统的Bloch振荡,使系统发生Landau-Zener隧穿,而不同自旋态流密度在动量空间分布的分离意味着自旋交换动力学的发生.

In a recent experiment[Hamner C,et al.2015 Phys.Rev.Lett.114070401],spin-orbit coupled Bose-Einstein condensates in a translating optical lattice have been successfully prepared into any Bloch band,and directly proved to be the lack of Galilean invariance in the presence of the spin-orbit coupling.The energy band structure of the system becomes complicated because of the lack of Galilean invariance.At present,the energy band structure of the spin-orbit coupled Bose-Einstein condensates in optical lattice is still an open issue,especially the theoretical evidence for the in-depth understanding of the competition mechanism among the spin-orbit coupling,the Raman coupling,the optical lattice and the atomic interactions of the nonlinear energy band structure has not been clear yet.In this paper,based on the two-mode approximation and variational analysis,the nonlinear energy band structure and current density of the spin-orbit coupled Bose-Einstein condensates in the one-dimensional optical lattice are investigated.We find that when the spin-orbit coupling,the Raman coupling,the optical lattice,and the atomic interactions satisfy certain conditions,a loop structure in the Brillouin zone edge will emerge.The critical condition for the loop structure emerging in the Brillouin zone edge is obtained in a parameter space.The Raman coupling and the optical lattice suppress the emergence of the loop structure,while the spin-orbit coupling and the atomic interactions promote the emerging of the loop structure and make the energy band structure more complex.Interestingly,the atomic interactions can make the loop structure occur at both the higher-lying bands and the lowest energy band.The energy band structure is closely related to the current density of the system.The spin-orbit coupling causes the current density to be strongly asymmetric and leads the current density distributions of different spin states to be separated from each other in the momentum space near the boundary of the Brillouin zone.The optical lattice strength and the Raman coupling can weaken the asymmetry.The appearance of loop structure breaks the Bloch oscillation and gives rise to the Landau-Zener tunneling.The separation of the current density distributions of different spin states in the momentum space means the emergence of the spin exchange dynamics.Our results are beneficial to the in-depth understanding of the nonlinear dynamics of the spin-orbit coupled Bose-Einstein condensates in optical lattice.