Exact analysis of the response of quantum systems to two-photons using a QSDE approach

We introduce the quantum stochastic differential equation (QSDE) approach to exactly analyze the response of quantum systems to a continuous-mode two-photon input. The QSDE description of the two-photon process allows us to integrate the input-output analysis with the quantum network theory, and so the analytical computability of the output state of a general quantum system can be addressed within this framework. We show that the time-domain two-photon output states can be exactly calculated for a large class of quantum systems including passive linear networks, optomechanical oscillators and two-level emitter in waveguide systems. In particular, we propose to utilise the results for the exact simulation of the stimulated emission as well as the study of the scattering of two-mode photon wave packets.