SU(2) Symmetry of Coherent Photons and Application to Poincaré Rotator

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 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.

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Cited by in corpus (6)

• Topological Polarisation States
• Photonic Quantum Chromo-Dynamics
• Spin of Photons: Nature of Polarisation
• Macroscopic Single-Qubit Operation for Coherent Photons
• Dirac Equation for Photons: Origin of Polarisation
• Macroscopic Singlet, Triplet, and Colour-Charged States of Coherent Photons