标题： 三维自旋轨道耦合玻色气体中的对称性保护的斯奎尔米ons 显示英文标题

标题： Symmetry protected skyrmions in 3D spin-orbit coupled Bose gases

摘要： 我们对谐波势中具有弱三维自旋轨道耦合的伪自旋$1/2$玻色气体进行了变分研究，该自旋轨道耦合属于$\bmsigma\cdot\mathbf{p}$类型。 这种自旋轨道耦合混合了不同宇称的状态，这启发我们用总角动量本征态来近似单粒子态，即谐波$s$波和$p$波状态的叠加。 由于时间反演对称性由两体相互作用保护，我们将变分序参量设置为总角动量的两个相互时间反演对称本征态的组合。 变分结果基本上再现了最近由 Kawakami{\it 等}识别的三维 Skyrmion 样基态。 我们表明，该模型中出现的这些 Skyrmion 样基态主要是由变分序参量中涉及的$p$波空间模式引起的，该模式驱动了两个自旋组分的空间分离。 我们发现该系统的基态根据同种与异种相互作用的相对大小落入两种具有不同密度分布对称性的相：相 I 具有宇称对称和轴对称的密度分布，而相 II 则以离散旋转对称性和时间反演对称性的特殊联合对称为特征。 随着相互作用强度的增加，在具有不同密度分布的两个相之间发生转变，而拓扑的三维 Skyrmion 样自旋结构则受到对称性的保护。 显示英文摘要

摘要： We present a variational study of pseudo-spin $1/2$ Bose gases in a harmonic trap with weak 3D spin-orbit coupling of $\bmsigma\cdot\mathbf{p}$ type. This spin-orbit coupling mixes states with different parities, which inspires us to approximate the single particle state with the eigenstates of the total angular momentum, i.e. superposition of harmonic $s$-wave and $p$-wave states. As the time reversal symmetry is protected by two-body interaction, we set the variational order parameter as the combination of two mutually time reversal symmetric eigenstates of the total angular momentum. The variational results essentially reproduce the 3D skyrmion-like ground state recently identified by Kawakami {\it et al.}. We show that these skyrmion-like ground states emerging in this model are primarily caused by $p$ wave spatial mode involving in the variational order parameter that drives two spin components spatially separated. We find the ground state of this system falls into two phases with different density distribution symmetries depending on the relative magnitude of intraspecies and interspecies interaction: Phase I has parity symmetric and axisymmetric density distributions, while Phase II is featured with special joint symmetries of discrete rotational and time reversal symmetry. With the increasing interaction strength the transition occurs between two phases with distinct density distributions, while the topological 3D skyrmion-like spin texture is symmetry protected.