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Proceedings Paper

Wigner distribution function for finite signals
Author(s): Kurt Bernardo Wolf; Natig M. Atakishiyev; Sergey M. Chumakov
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Paper Abstract

We construct a bilinear form with the properties of the Wigner distribution function for a model of finite optics: the multimodal linear waveguide. This is a guide that can carry a finite number of oscillator modes, and sends/reads the data by an equal number of sensors. The Wigner distribution function is a function of the classical observables of position and momentum, as well as the mode content; it provides a visual image corresponding to the (`musical') score of the signal. The dynamical group for this model is SU(2) and the wavefunctions span the space of a finite-dimensional irreducible representation of this group. Phase space is a sphere and the linear optical transformations are: translations along the waveguide, refractive wedges and inclined slabs, which correspond to rotations around the 3-, 1-, and 2-axes, respectively. Coherent and Schrodinger cat states are readily identified.

Paper Details

Date Published: 1 July 1997
PDF: 11 pages
Proc. SPIE 3076, Photonic Quantum Computing, (1 July 1997); doi: 10.1117/12.277653
Show Author Affiliations
Kurt Bernardo Wolf, Univ. Nacional Autonoma de Mexico (Mexico)
Natig M. Atakishiyev, Univ. Nacional Autonoma de Mexico (Mexico)
Sergey M. Chumakov, Univ. Nacional Autonoma de Mexico (Mexico)


Published in SPIE Proceedings Vol. 3076:
Photonic Quantum Computing
Steven P. Hotaling; Andrew R. Pirich, Editor(s)

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