Quantum theory of light and noise polarization in nonlinear optics

Abstract

We present a consistent quantum theory of the electromagnetic field in nonlinearly responding causal media, with special emphasis on $χ^{(2)}$ media. Starting from QED in linearly responding causal media, we develop a method to construct the nonlinear Hamiltonian expressed in terms of the complex nonlinear susceptibility in a quantum mechanically consistent way. In particular we show that the method yields the nonlinear noise polarization, which together with the linear one is responsible for intrinsic quantum decoherence.