  We introduce the quantum stochastic differential equation (QSDE) approach to
exactly analyze of 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 utilize the results for the
exact simulation of the stimulated emission as well as the study of the
scattering of two-mode photon wave packets.

Quantum Physics