Quantum theory of light in nonlinear media with dispersion and absorption

We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a-microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.