Interferometers and Decoherence Matrices

Abstract

It is shown that the Lorentz group is the natural language for two-beam interferometers if there are no decoherence effects. This aspect of the interferometer can be translated into six-parameter representations of the Lorentz group, as in the case of polarization optics where there are two orthogonal components of one light beam. It is shown that there are groups of transformations which leave the coherency or density matrix invariant, and this symmetry property is formulated within the framework of Wigner's little groups. An additional mathematical apparatus is needed for the transition from a pure state to an impure state. Decoherence matrices are constructed for this process, and their properties are studied in detail. Experimental tests of this symmetry property are possible.

RevTex 14 pages, no figures

References in corpus (2)

• Representations of the Weyl group and Wigner functions for SU(3)
• Wigner Rotations and Iwasawa Decompositions in Polarization Optics

Cited by in corpus (8)

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• Binary Representations of ABCD Matrices
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• ABCD Matrices as Similarity Transformations of Wigner Matrices and Periodic Systems in Optics
• Lorentz group theory and polarization of the light
• Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms
• Transitivity in the theory of the Lorentz group and the Stokes -- Mueller formalism in optics