Schrödinger soliton in a fiber waveguide exhibiting both gain and losses: squeezed states and growth of noise in the linear approximation

An investigation is made of the evolution of quantum fluctuations of a fundamental soliton in the course of its propagation in a nonlinear fiber waveguide characterized by losses and compensated by amplification. Simple relationships are obtained for the amplitude and phase noise, quantum uncertainty of the position and momentum, and also fluctuations of the quadrature components of the radiation field. Numerical estimates are obtained. It is shown that loss-compensating amplification is unnecessary for efficient formation of squeezed states of a soliton.