On the Spectrum of Field Quadratures for a Finite Number of Photons

Details On the Spectrum of Field Quadratures for a Finite Number of Photons On the Spectrum of Field Quadratures for a Finite Number of Photons

2011-09-26

arxiv.org/abs/1109.5724v1

Physics

Quantum Physics

14 pages, 11 figures

Scientific paper

The spectrum and eigenstates of any field quadrature operator restricted to a finite number N of pho- tons are studied, in terms of the Hermite polynomials. By (naturally) defining approximate eigenstates, which represent highly localized wavefunctions with up to N photons, one can arrive at an appropriate notion of limit for the spectrum of the quadrature as N goes to infinity, in the sense that the limit coincides with the spectrum of the infinite-dimensional quadrature operator. In particular, this notion allows the spectra of truncated phase operators to tend to the complete unit circle, which is what one would expect, in contrast to what has been previously reported. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.

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