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Physical Review

A Stokes-Parameter Technique for the Treatment of Polarization in Quantum Mechanics

U. Fano

Published Jan 1, 1954• 164 citations
Publisher

Abstract

A technique is presented which adapts the Stokes method to quantum mechanics and serves to calculate polarization effects by means of Pauli matrices. Illustrative examples indicate that this technique may be not only convenient mathematically but also physically more transparent than previous methods.
DOI
10.1103/physrev.93.121

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It is shown that the description of polarization based on quantization of classical Stokes parameters is incomplete in quantum domain. For example, the polarization of the electric dipole radiation of the atomic or molecular transitions is described by nine generators of the SU(3) subalgebra in the Weyl-Heisenberg algebra of photons, in other words, by nine independent Stokes operators instead of four dependent classical Stokes parameters. Although some of the Stokes operators have one and the same averages, they describe absolutely different physical quantities with strongly different quantum fluctuations. The quantum polarization properties of the electric dipole and quadrupole radiation are examined as a function of distance for the near, intermediate, and far zones. Application of results in the near-field optics and quantum entanglement research is discussed.
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This paper introduces a novel approach to geometry modeling utilizing nonlinear quantum adaptive geometry transformations. We propose a method that transforms complex geometric models into adaptable geometric models, enabling self-adaptive deformation within the model. The core mechanism involves a quantum process that dynamically adjusts geometric parameters based on a feedback loop, resulting in a highly flexible and responsive model. This approach offers significant advantages over traditional methods, particularly in handling intricate geometries and complex deformations. This research addresses the limitations of existing techniques by introducing a fundamentally new method that leverages quantum mechanics to achieve a level of adaptability not previously attainable. This work demonstrates the feasibility and potential of this approach through mathematical analysis and illustrative examples.