  In this work, we discuss connections between different theoretical physics
communities and their works, all related to systems that act as sources of
particles such as photons, phonons, or electrons. Our interest is to understand
how a low-dimensional quantum system driven by coherent fields, e.g. a
two-level system, Jaynes-Cummings system, or photon pair source driven by a
laser pulse, emits photons into a waveguide. Of particular relevance to
solid-state sources is that we provide a way to include dissipation into the
formalism for temporal-mode quantum optics. We will discuss the connections
between temporal-mode quantum optics, scattering matrices, quantum stochastic
calculus, continuous matrix product states and operators, and very traditional
quantum optical concepts such as the Mandel photon counting formula and the
Lindblad form of the quantum-optical master equation. We close with an example
of how our formalism relates to single-photon sources with dephasing.

Quantum Physics;Atomic Physics;Optics