A1 Refereed original research article in a scientific journal
Covariant phase observables
Authors: Pellonpaa JP
Publisher: WILEY-V C H VERLAG GMBH
Publication year: 2003
Journal:: Fortschritte der Physik / Progress of Physics
Journal name in source: FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
Journal acronym: FORTSCHR PHYS
Volume: 51
Issue: 2-3
First page : 207
Last page: 210
Number of pages: 4
ISSN: 0015-8208
DOI: https://doi.org/10.1002/prop.200310028
Abstract
Covariant phase observables constitute a simple solution of the quantum phase problem of a single-mode optical field. They share three important properties: their range of values is the phase interval [0, 2pi), they are covariant under shifts generated by the number operator (which is necessary for coherent state phase measurements), and they have the uniform phase distribution in number states. Moreover, some phase observables have been measured (e.g. the phase observable associated to the Q-function). The canonical phase observable has some additional properties which distinguish it from other covariant phase observables: it generates number shifts, it is uniquely associated to the polar decomposition of the lowering operator (Dirac's idea [1]), it has a projection valued covariant dilation (Newton's extension [2]), and it has a projection valued discretization. (the Pegg-Barnett formalism [3]). The single-mode covariant phase theory can easily be extended to the two-mode theory of covariant phase difference observables. Finally, most of all phase theories have connections to the covariant phase theory.
Covariant phase observables constitute a simple solution of the quantum phase problem of a single-mode optical field. They share three important properties: their range of values is the phase interval [0, 2pi), they are covariant under shifts generated by the number operator (which is necessary for coherent state phase measurements), and they have the uniform phase distribution in number states. Moreover, some phase observables have been measured (e.g. the phase observable associated to the Q-function). The canonical phase observable has some additional properties which distinguish it from other covariant phase observables: it generates number shifts, it is uniquely associated to the polar decomposition of the lowering operator (Dirac's idea [1]), it has a projection valued covariant dilation (Newton's extension [2]), and it has a projection valued discretization. (the Pegg-Barnett formalism [3]). The single-mode covariant phase theory can easily be extended to the two-mode theory of covariant phase difference observables. Finally, most of all phase theories have connections to the covariant phase theory.
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