Spin structure of harmonically trapped one-dimensional atoms with spin-orbit coupling
Spin structure of harmonically trapped one-dimensional atoms with spin-orbit coupling
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DOI：
10.1103/physreva.92.023641
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发表时间：
2015-08
影响因子：
2.9
通讯作者：
Q. Guan;D. Blume
中科院分区：
文献类型：
--
作者：
Q. Guan;D. Blume
我们引入了一种理论方法来确定具有二体零程相互作用的谐波捕获原子的自旋结构，该相互作用受到通过原子超精细态拉曼耦合创建的 Rashba 和 Dresselhaus 自旋轨道耦合的等量混合。计算了具有有限和无限二体相互作用强度 $g$ 的玻色子和费米子双粒子系统的自旋结构。利用具有无限大耦合强度$g$的$N$-玻色子和$N$-费米子系统可分析求解消失的自旋轨道耦合强度$k_{so}$和消失的拉曼耦合强度$\Omega$这一事实，我们开发了一个有效的自旋模型，对于任何$k_{so}$和无限$g$，该模型在$\Omega$中精确到二阶。明确考虑三粒子和四粒子系统。结果表明，有效自旋哈密顿量包含海森堡交换项和各向异性 Dzyaloshinskii-Moriya 交换项，将这些系统随着 $k_{so}$ 的变化而经历的转变描述为独立自旋动力学和最近邻自旋相互作用之间的竞争。
We introduce a theoretical approach to determine the spin structure of harmonically trapped atoms with two-body zero-range interactions subject to an equal mixture of Rashba and Dresselhaus spin-orbit coupling created through Raman coupling of atomic hyperfine states. The spin structure of bosonic and fermionic two-particle systems with finite and infinite two-body interaction strength $g$ is calculated. Taking advantage of the fact that the $N$-boson and $N$-fermion systems with infinitely large coupling strength $g$ are analytically solvable for vanishing spin-orbit coupling strength $k_{so}$ and vanishing Raman coupling strength $\Omega$, we develop an effective spin model that is accurate to second-order in $\Omega$ for any $k_{so}$ and infinite $g$. The three- and four-particle systems are considered explicitly. It is shown that the effective spin Hamiltonian, which contains a Heisenberg exchange term and an anisotropic Dzyaloshinskii-Moriya exchange term, describes the transitions that these systems undergo with the change of $k_{so}$ as a competition between independent spin dynamics and nearest-neighbor spin interactions.