Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Mota, R. D.
Xicotencatl, M. A.
Granados, V. D.
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In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown {\it a priori}. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman SU(3) symmetry group matrices. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that generalized Stokes Operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization density matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical three-dimensional isotropic harmonic oscillator we describe the geometric properties of the polarization ellipse
Mathematical Physics, 42.50.-p, 42.25.-p, 42.25.Ja, 11.30.-j, 03.65.Fd