SU(2) symmetry of coherent photons and application to Poincaré rotator
SU(2) symmetry of coherent photons and application to Poincaré rotator
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DOI：
10.3389/fphy.2023.1225419
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发表时间：
2023-03
影响因子：
3.1
通讯作者：
S. Saito
中科院分区：
文献类型：
--
作者：
S. Saito
李代数是一种隐藏在自然界各种量子系统背后的数学结构。本文考虑从激光源发射的相干光子偏振态的SU(2)波函数，并基于同构定理讨论了具有SO(3)对称性的自旋期望值与SU(2)波函数的关系。特别是，我们发现旋转的半波片对应于庞加莱球中的镜像反射，由于反厄米特性质，它们在投影的O(2)平面中不会形成子群。这可以在实验上通过制备另一个半波片来实现SU(2)中的原始旋转器来克服，该旋转器允许由物理旋转决定任意旋转角度。通过结合另外2个四分之一波片，我们也可以构造一个真正的移相器，从而实现对整个庞卡勒球的被动控制。
Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. Here, we consider SU(2) wavefunctions for polarisation states of coherent photons emitted from a laser source, and discuss the relationship to spin expectation values with SO(3) symmetry based on isomorphism theorems. In particular, we found rotated half-wave-plates correspond to mirror reflections in the Poincaré sphere, which do not form a subgroup in the projected O(2) plane due to anti-hermitian property. This could be overcome experimentally by preparing another half-wave-plate to realise a pristine rotator in SU(2), which allows arbitrary rotation angles determined by the physical rotation. By combining another 2 quarter-wave-plates, we could also construct a genuine phase-shifter, thus, realising passive control over the full Poincaré sphere.