  We develop a quantum reductive perturbation method (RPM), a generalization of
classical RPM widely used in nonlinear wave theory, to derive a simplified
model (i.e. quantum nonlinear Schrodinger equation) from fully quantum
Heisenberg-Langevin-Maxwell equations describingphoton propagations in a
coherent cold atomic gas. The result is used to discuss two-photon bound states
and optical solitons in the gas. Though a specific system is considered, the
quantum RPM established here is very general and can be applied to other
complex quantum nonlinear problems.
