Cumulant expansion for studying damped quantum solitons

The quantum statistics of damped optical solitons is studied using cumulant -expansion techniques. The effect of absorption is described in terms of or dinary Markovian relaxation theory, by coupling the optical field to a cont inuum of reservoir modes. After introduction. of local bosonic field operat ors and spatial discretization, pseudo-Fokker-Planck equations for multidim ensional s-parametrized phase-space functions are derived. These partial di fferential equations are equivalent to an infinite set of ordinary differen tial equations for the cumulants of the phase-space functions. Introducing an appropriate truncation condition, the resulting finite set of cumulant e volution equations can be solved numerically. Solutions are presented in a Gaussian approximation and the quantum noise is calculated. with special em phasis on squeezing and the recently measured spectral photon-number correl ations [Spalter et al., Phys. Rev. Lett. 81, 786 (1998)]. [S1050-2947(99)06 703-7].