Making use of c-number stochastic theory and soliton perturbation theory, we study the quantum fluctuations of a self-induced transparency (SIT) soliton propagating through a lossless two-level medium. Considering the fluctuations as small corrections to the classical soliton, we are able to construct and solve four stochastic equations that govern the evolution of four soliton parameters: photon number (intensity), phase, timing, and momentum (frequency). We find excellent agreement between our stochastic theory of SIT solitons and the second-quantized theory of Lai and Haus [Phys. Rev. A 42, 2925 (1990)].
© 2000 Optical Society of America
Victor V. Kozlov and Andrey B. Matsko, "Stochastic theory of self-induced transparency: linearized approach," J. Opt. Soc. Am. B 17, 1031-1038 (2000)