Quantum fluctuations of one- and two-dimensional spatial dissipative solitons in a nonlinear interferometer: II. Two-dimensional light solitons
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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.
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