论文标题
超高原子的定位在不相称的自旋 - 轨耦合和Zeeman晶格中
Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
论文作者
论文摘要
我们认为由一维哈密顿量支配的粒子，在该粒子中，人工周期性的自旋轨道耦合和Zeeman晶格具有不相称的周期。使用对这种准二元的哈密顿量的最佳理性近似，该问题降低为对超晶格中的旋转状态的描述。在没有恒定的Zeeman分裂的情况下，系统将获得额外的对称性，从而阻碍了本地化。但是，如果晶格足够深，那么即使是平均值为零或小值的Zeeman字段，局部状态也可以出现。局部模式的空间分布几乎是均匀的，与有效超晶格的拓扑特性直接相关：模式的质量坐标是由从超晶格带结构计算出的ZAK阶段确定的。最佳理性近似具有“内存”效应：每个有理近似都保留有关先前获得的模式的能量和空间分布的信息，较不准确的近似值。低能量初始波袋的分散为特征，其特征是法律$ \ propto t^β$，$β$在初始阶段的$ 1/2 $之间变化，更长的$ 1 $在$ 1/2 $之间，但仍有有限的时间变化。初始波袋的动力学（令人兴奋的主要局部模式）表现出量子复兴。
We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the problem is reduced to description of spinor states in a superlattice. In the absence of a constant Zeeman splitting, the system acquires an additional symmetry, which hinders the localization. However, if the lattices are deep enough, then localized states can appear even for Zeeman field with zero or small mean value. Spatial distribution of localized modes is nearly uniform and is directly related to the topological properties of the effective superlattice: center-of-mass coordinates of modes are determined by Zak phases computed from the superlattice band structure. The best rational approximations feature the `memory' effect: each rational approximation holds the information about the energies and spatial distribution of the modes obtained under preceding, less accurate approximations. Dispersion of low-energy initial wavepackets is characterized by the law $\propto t^β$ with $β$ varying between $1/2$ at the initial stage and $1$ at longer, but still finite-time, evolution. The dynamics of initial wavepackets, exciting mainly localized modes, manifests quantum revivals.
