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

R D Mota1, M A Xicoténcatl2 and V D Granados3

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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 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 matrices of the SU(3) symmetry group. 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 the generalized Stokes operators together with the Gell–Mann and Ne'eman matrices may be used to expand the polarization 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 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.


PACS

42.50.-p Quantum optics

42.25.Ja Polarization

03.65.Fd Algebraic methods

MSC

35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)

20B30 Symmetric groups

Subjects

Optics, quantum optics and lasers

Quantum information and quantum mechanics

Dates

Issue 7 (20 February 2004)

Received 3 July 2003

Published 4 February 2004



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