  We analyze the quantum dynamics of radiation propagating in a single mode
optical fiber with dispersion, nonlinearity, and Raman coupling to thermal
phonons. We start from a fundamental Hamiltonian that includes the principal
known nonlinear effects and quantum noise sources, including linear gain and
loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are
treated. This allows quantum Langevin equations to be calculated, which have a
classical form except for additional quantum noise terms. In practical
calculations, it is more useful to transform to Wigner or +$P$
quasi-probability operator representations. These result in stochastic
equations that can be analyzed using perturbation theory or exact numerical
techniques. The results have applications to fiber optics communications,
networking, and sensor technology.
