Quantum field fluctuations in the vicinity of a classical laser soliton

Abstract

An analysis of weak quantum fluctuations of a spatial soliton in a laser with fast saturable absorption in the possible presence of weak holding radiation is carried out. In the c-number representation with adiabatic elimination of atomic variables, the master Heisenberg–Langevin equation is linearized in the vicinity of a stable classical (in the absence of fluctuations) laser soliton. The linearized equation’s solution is constructed on the basis of the spectral expansion in eigenfunctions of the evolution operator unperturbed by fluctuations. The discrete spectrum of this operator is found and used to determine the mean values of the squared fluctuations of the coordinates of the soliton center and its momentum. A comparison is made with similar fluctuations in driven interferometers with Kerr non-linearity of the medium.