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 ${\chi }^{(2)}$ media. Starting from QED in linearly responding causal media, we develop a method to construct the cubic 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.