A quantum theory of nonlinear propagation of Shroedinger's solitons - Squeezed states and sub-Poisson statistics

A quantum theory of propagation of solitons in a nonlinear medium is developed based on Shroedinger's nonlinear equation for operators of positive and negative frequency parts of the field. The equation is derived in the continual-integral representation, a form useful in the analysis of the dynamics of quantum field fluctuations. An analysis is presented of the propagation of a fundamental soliton initially in the coherent state, and it is shown that the photon statistics of a soliton in a nonlinear medium does not change. It is also shown that under certain conditions fluctuations of one of the quadrature components of the field may be suppressed. Interference between the soliton and coherent radiation alters the photon statistics of the resulting field. The conditions for optimal suppression of the fluctuations of photon number and under which their sub-Poisson statistics occur are considered.