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Covariant phase observables
Tekijät: Pellonpaa JP
Kustantaja: WILEY-V C H VERLAG GMBH
Julkaisuvuosi: 2003
Lehti:: Fortschritte der Physik / Progress of Physics
Tietokannassa oleva lehden nimi: FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
Lehden akronyymi: FORTSCHR PHYS
Vuosikerta: 51
Numero: 2-3
Aloitussivu: 207
Lopetussivu: 210
Sivujen määrä: 4
ISSN: 0015-8208
DOI: https://doi.org/10.1002/prop.200310028
Tiivistelmä
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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