Femtosecond solitons in nonlinear optical fibers: Classical and quantum effects

We use the time-dependent Hartree approximation to obtain solutions to a quantized higher-order nonlinear Schr\"odinger equation. This equation describes pulses propagating in nonlinear-optical fibers and, under certain conditions, has femtosecond soliton solutions. These solitons travel at velocities that differ from those of the picosecond solitons obtained from the standard quantized nonlinear Schr\"odinger equation. Furthermore, we find that quadruple-clad fibers are required for the propagation of these solitons, unlike the solitons of the standard nonlinear Schr\"odinger equation, which can propagate in graded-index optical fibers. From the quantum solution, we find that the soliton experiences phase spreading and self-squeezing as it propagates.