Causal Nonlinear Quantum Optics

Ullrich Martini, Christian Wagner, Axel Schenzle

Xuesong Gao

Stefan Scheel, D.‐G. Welsch

We present a quantization scheme for the electromagnetic field in locally responding nonlinear dielectric materials with dispersion and absorption. Based on the Green tensor expansion of the macroscopic electromagnetic field, we derive an expression for the nonlinear polarization that contains, besides the reactive part which is responsible for the nonlinear interaction, a noise contribution that has hitherto been disregarded. For the process of third-harmonic generation, we find that the magnitude of the nonlinear noise polarization is proportional to the intensity of the pump fields.

Stefan Scheel, Dirk‐Gunnar Welsch

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.

Eiichi Hanamura, Yutaka Kawabe, Akio Yamanaka