Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms

Date
1995-10-15
Advisor
Instructor
Source Title
Optics Communications
Print ISSN
0030-4018
Electronic ISSN
1873-0310
Publisher
Elsevier BV * North-Holland
Volume
120
Issue
3-4
Pages
166 - 170
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

It is customary to define a phase space such that position and momentum are mutually orthogonal coordinates. Associated with these coordinates, or domains, are the position and momentum operators. Representations of the state vector in these coordinates are related by the Fourier transformation. We consider a continuum of "fractional" domains making arbitrary angles with the position and momentum domains. Representations in these domains are related by the fractional Fourier transformation. We derive transformation, commutation, and uncertainty relations between coordinate multiplication, differentiation, translation, and phase shift operators making arbitrary angles with each other. These results have a simple geometric interpretation in phase space and applications in quantum optics.

Course
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Book Title
Keywords
Computational methods, Fourier transforms, Mathematical models, Phase space methods, Fractional Fourier transforms, Orthogonal coordinates, Quantum optics
Citation
Published Version (Please cite this version)