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Physical Review A

Transverse distribution of quantum fluctuations and correlations in spatial solitons

Nicolas Treps, Claude Fabre

Published Aug 17, 2000• 18 citations
Publisher

Abstract

We give in this paper a general method by which to determine the transverse spatial distribution of quantum fluctuations in a light beam as it propagates through a nonlinear medium. We apply this method to the particular case of spatial solitons that propagate without distortion in ${\ensuremath{\chi}}^{(2)}$ or ${\ensuremath{\chi}}^{(3)}$ materials. We find, for example, that in the ${\ensuremath{\chi}}^{(2)}$ case the central part of the soliton has lower intensity quantum fluctuations than its outer part, and that in most cases strong correlations develop among the field quadrature components measured in different areas of the transverse plane.

DOI
10.1103/physreva.62.033816

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Quantum fluctuations of two-dimensional dark dissipative solitons in an interferometer filled with a Kerr nonlinear medium are analyzed theoretically. The boundaries of the stability region of classical solitons excited in the considered interferometer by an external radiation are refined. The solution of the quantum problem is studied in the linear approximation. For this purpose, the formalism of expansion of the sought solution in discrete spectral functions is extended to the two-dimensional case. Using this expansion made it possible to construct a solution that describes fluctuations of collective variables of a two-dimensional soliton, namely, the coordinate of the center and momentum. Mean squares of quantum fluctuations of these quantities are calculated. Parameter domains in which there exist squeezed states of solitons with respect to each of the collective variables are determined. Comparative analysis of squeezing with respect to these variables for light and dark solitons is performed.