Few-photon scattering and emission from open quantum systems

We show how to use the input-output formalism compute the propagator for an open quantum system, i.e. quantum networks with a low dimensional quantum system coupled to one or more loss channels. The total propagator is expressed entirely in terms of the Green's functions of the low dimensional quantum system, and it is shown that these Green's functions can be computed entirely from the evolution of the low-dimensional system with an effective non-hermitian Hamiltonian. Our formalism generalizes the previous works that have focused on time independent Hamiltonians to systems with time dependent Hamiltonians, making it a suitable computational tool for the analysis of a number of experimentally interesting quantum systems. We illustrate our formalism by applying it to analyze photon emission and scattering from driven and undriven two-level system and three- level lambda system.