SU(2) symmetry of coherent photons and application to Poincaré rotator

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 isomor...

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Bibliographic Details
Published inFrontiers in physics Vol. 11
Main Author Saito, Shinichi
Format Journal Article
LanguageEnglish
Published Frontiers Media S.A 07.07.2023
Subjects
coherent state
Poincaré sphere
polarisation
spin angular momentum
Stokes parameters
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Summary: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.
ISSN:2296-424X
2296-424X
DOI:10.3389/fphy.2023.1225419