Abstract
The Heisenberg–Langevin equation for a spatial laser soliton is constructed within consistent quantum electrodynamics. Canonical variables for the generation field and for a two-level material medium consisting of a medium that generates a laser and a medium that realizes saturable absorption are discussed in detail. It is assumed that the laser generation evolves in time much more slowly than the atomic medium. This makes it possible to apply the adiabatic approximation and construct a closed equation for the amplitude of the laser field. The equation has been derived paying special attention to the definition of Langevin sources, which play a decisive role in the formation of quantum statistical features of solitons. To ensure the observation procedure of the quantum squeezing of a soliton, the laser generation has been synchronized by applying an external weak electromagnetic field.
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