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Factorisation of analytic representations in the unit disk and number-phase statistics of a quantum harmonic oscillator

A. Vourdas·C. Brif·A. Mann
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Abstract

The inner-outer part factorisation of analytic representations in the unit disk is used for an effective characterisation of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorisation is intimately connected to the number-phase Weyl semigroup and its properties. In the Barut-Girardello analytic representation the factorisation is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorisation and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorisation properties of a superposition state.

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A. Vourdas, C. Brif, A. Mann. 1996-06-22. Factorisation of analytic representations in the unit disk and number-phase statistics of a quantum harmonic oscillator. https://doi.org/10.1088/0305-4470/29/18/018

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