SU(2) Symmetry of Coherent Photons and Application to Poincar\'e Rotator

• URL: http://arxiv.org/abs/2303.18199v1
• Date: Thu, 30 Mar 2023 03:49:42 GMT
• Title: SU(2) Symmetry of Coherent Photons and Application to Poincar\'e Rotator
• Authors: Shinichi Saito
• Abstract summary: Lie algebra is a hidden mathematical structure behind quantum systems realised in nature. We consider $SU(2)$ wavefunctions for polarisation states of coherent photons emitted from a laser source.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Poincar\'e 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 Poincar\'e sphere.

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