Few-photon scattering and emission from low-dimensional quantum systems

We show how to use the input-output formalism to compute the propagator for a low-dimensional quantum system coupled to an optical field under the rotating wave and Markovian approximation. The propagator for this coupled system is expressed in terms of the Green's functions of the low-dimensional system, and it is shown that these Green's functions can be computed entirely from the evolution of the low-dimensional system under an effective non-Hermitian Hamiltonian. Our formalism generalizes the previous works that have focused on time-independent Hamiltonians to systems with time-dependent Hamiltonians (e.g., coherently driven systems), 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 the driven and undriven two-level system and the three-level lambda system.