Thursday, September 6, 2012

1109.5724 (Emilio Pisanty et al.)

On the Spectrum of Field Quadratures for a Finite Number of Photons    [PDF]

Emilio Pisanty, Eduardo Nahmad-Achar
The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \textit{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, as one would expect. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.
View original: http://arxiv.org/abs/1109.5724

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