We theoretically study the generation of orbital angular momentum (OAM) based on the four-wave mixing process in a diamond-type homogeneously broadened $^{85}{\rm Rb}$ atomic system. We use density matrix formalism at a weak field limit to explain the origin of vortex translation between different optical fields and a generated signal. We show how the singularities, which are omnipresent in the phases of the input optical vortex beams, can be profoundly mapped to atomic coherence in the transverse plane, which holds the origin of OAM translation. This translation process works well even for a moderately intense probe and control field, which enhances medium nonlinearity. The generation and manipulation of OAM of the light beam in a nonlinear medium may have important applications in optical tweezers and quantum information processing systems.

中文翻译：

---

基于四波混合的轨道角动量平移

我们从理论上研究了在钻石型均匀加宽的$ ^ {85} {\ rm Rb} $中基于四波混合过程的轨道角动量（OAM）的产生原子系统。我们在弱场限制下使用密度矩阵形式来解释不同光场和生成信号之间涡旋平移的起源。我们展示了如何在输入光学涡旋光束的相位中普遍存在的奇异性可以深刻地映射到横向平面中的原子相干性，从而保持了OAM平移的起源。即使对于中等强度的探测和控制场，此转换过程也能很好地工作，从而增强了介质的非线性。非线性介质中光束的OAM的生成和操纵可能在光镊和量子信息处理系统中具有重要的应用。