Squeezing of quantum solitons

We develop a quantum theory of propagation in dispersive nonlinear media. Quantum fluctuations are handled via the coherent-state positive-P representation. A stochastic nonlinear Schrödinger equation in the field variables is obtained which predicts wide band squeezing in the region of anomalous dispersion. For soliton inputs, fluctuations are reduced over the soliton bandwidth. This leads to quantum solitons which have quadrature fluctuations less than the level of vacuum fluctuations.