Particle emission from open-quantum systems

Abstract: 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.