On The Scattering Process in Quantum Optics

The derivation of a quantum Markovian model for an opto-mechanical system consisting of a quantum mechanical mirror interacting with quantum optical input fields via radiation pressure is difficult problem which ultimately involves the scattering process of quantum stochastic calculus. We show that while the scattering process may be approximated in a singular limit by regular processes using different schemes, however the limit model is highly sensitive to how the approximation scheme is interpreted mathematically. We find two main types of stochastic limits of regular models, and illustrate the origin of this difference at the level of one particle scattering. As an alternative modelling scheme, we consider models of mirrors as non-trivial dielectric medium with a boundary that is itself quantized. Rather than treating the plane waves for the electromagnetic field, we take the actual physical modes and quantize these. The input-output formalism is then obtained in the far zone where the plane wave approximation is valid. Several examples are considered, and the quantum stochastic model is derived. We also consider the quantum trajectories problem for continual measurement of the reflect output fields, and derive the stochastic master equations for homodyning and photon counting detection to estimate the mirror observables.