近日，墨西哥蒙特雷理工学院的B. Perez-Garcia与墨西哥帕丘卡理工大学的B. M. Rodríguez-Lara等人合作并取得一项新进展。经过不懈努力，他们对光学标量光束和矢量场的马约拉纳星座进行了研究。相关研究成果已于2024年12月23日在国际知名学术期刊《物理评论A》上发表。

该团队研究了利用光的自旋和轨道角动量，在黎曼球面上对光标量束和矢量场，进行马约拉纳恒星表示的方法。在此框架下，标量拉盖尔-高斯光束基的恒星星座出现在球面的两极，而矢量场的恒星星座则对应于明确的圆极化状态。

通过利用角动量的su(2)对称性，研究人员对基元进行了广义幺正旋转，从而在球面上生成了标量束和矢量场的光学布洛赫态，和广义su(2)相干态的类似物。这些旋转使得标量厄米-高斯光束，和限制在线性极化的矢量厄米-高斯部分庞加莱场的恒星星座，沿着球面的赤道排列。研究人员还解决了逆问题，即从恒星星座重构光学标量束和矢量场。

此外，研究人员探索了标量和矢量形式的猫态码，和量子性之王态的类似物，为复杂光学束和场的可视化和特征描述提供了帮助。这些见解表明，该方法在光通信领域具有潜在的应用价值。

附：英文原文

Title: Majorana constellations for optical scalar beams and vector fields

Author: F. Torres-Leal^1,*, E. García Herrera^1,*, M. P. Morales Rodríguez^2,*, B. Perez-Garcia^1,†, and B. M. Rodríguez-Lara^3,‡,§

Issue&Volume: 2024-12-23

Abstract: We explore the Majorana stellar representation on the Riemann sphere for optical scalar beams and vector fields, utilizing the spin and orbital angular momentum of light. In this framework, star constellations for a scalar Laguerre-Gaussian beam basis appear at the poles of the sphere, while those for vector fields correspond to well-defined circular polarizations. Leveraging the su(2) symmetry of angular momentum, we populate the sphere through generalized unitary rotations of basis elements, producing optical analogs of Bloch and generalized su(2) coherent states for both scalar beams and vector fields. These rotations position constellations for scalar Hermite-Gaussian beams and vector Hermite-Gaussian partial Poincaré fields, restricted to linear polarization, along the equator of the sphere. We also address the inverse problem, reconstructing optical scalar beams and vector fields from their stellar constellations. Additionally, we explore scalar and vector analogs of cat codes and kings of quantumness, contributing to the visualization and characterization of complex optical beams and fields. These insights suggest potential applications in optical communications.

DOI: 10.1103/PhysRevA.110.063716

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.063716