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arXiv:quant-ph/0311088 · Journal of Optics B Quantum and Semiclassical Optics

Quantum fluctuations and correlations of spatial scalar or multimode vector solitons in Kerr media

Éric Lantz, Thibaut Sylvestre, H. Maillotte, Nicolas Treps, Claude Fabre

Published May 1, 2004• 17 citations
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Abstract

We apply the Green function method to determine the global degree of squeezing and the transverse spatial distribution of quantum fluctuations of solitons in Kerr media. We show that both scalar bright solitons and multimode vector solitons experience strong squeezing on the optimal quadrature. For vector solitons, this squeezing is shown to result from an almost perfect anti-correlation between the fluctuations in the two incoherently coupled circular polarizations.

DOI
10.1088/1464-4266/6/5/018

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We apply the Green function method to determine the global degree of squeezing and the transverse spatial distribution of quantum fluctuations of solitons in Kerr media. We show that both scalar bright solitons and multimode vector solitons experience strong squeezing on the optimal quadrature. For vector solitons, this squeezing is shown to result from an almost perfect anti-correlation between the fluctuations in the two incoherently coupled circular polarizations.
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.
Summary form only given. The quantum properties of the interaction between an electromagnetic field and a nonlinear media have been widely studied, theoretically and experimentally, but so far these studies concerned mainly measurements performed on the total intensity of light beams, integrated over all the transverse plane. However, the details of the noise distribution inside the transverse plane, as well as the spatial quantum correlation between two different points, can be also very instructive, on a fundamental side in order to understand the propagation of the quantum noise, but also on a practical side to generate special configurations of the field which allow us to increase the spatial resolution of measurements in the transverse plane. We study here the spatial properties of the quantum fluctuations for a field freely propagating in a thick nonlinear medium, and in a case where the interaction distance is not limited by the diffraction : the spatial soliton regime, where diffraction effects are counterbalanced by nonlinearity and which exists in /spl chi//sup (2)/ and /spl chi//sup (3)/ media.
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.
The dynamical behavior of Kerr optical frequency combs is very well understood today from the perspective of the semi-classical approximation. In this article, we provide a theoretical understanding of the phenomena of quantum correlations, multimode entanglement and squeezed states of light that can occur in these frequency combs when quantum noise is accounted for. We prove that for all stationary spatio-temporal patterns, the side-modes that are symmetrical relatively to the central (pumped) mode in the frequency domain display quantum correlations that can lead to squeezed states of light under some optimal conditions that are analytically determined. We show that these quantum correlations can persist regardless the dynamical state of the system (rolls or solitons), regardless of the spectral extension of the comb (number sidemodes), and regardless of the dispersion regime (normal or anomalous). We study with particular emphasis the two principal architectures for Kerr comb generation, namely the add-through and add-drop configurations. We show that in both cases, the ratio between out-coupling and total losses plays a key role as it directly determines the efficiency of the squeezing. We also explicitly determine the phase quadratures leading to photon entanglement, and analytically calculate their quantum noise spectra. The relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths is also discussed.