Ab initio few-mode theories for quantum potential scattering problems

Few-mode models have been a cornerstone of the theoretical work in quantum optics, with the famous single-mode Jaynes-Cummings model being only the most prominent example. In this work, we present a method to derive exact few-mode Hamiltonians for quantum potential scattering problems, connecting system-bath models to ab initio theory. We demonstrate how to rigorously reconstruct the scattering matrix from such few-mode Hamiltonians, and show that upon inclusion of a background scattering contribution, an ab initio version of the well known input-output formalism is equivalent to standard scattering theory. Our results demonstrate that few-mode as well as input-output models can be extended to a general class of quantum scattering problems, and open up the associated tool-box to be applied to various platforms and extreme regimes, such as cavity quantum electrodynamics beyond the good cavity regime, electronic transport in mesoscopic systems as well as tunneling physics. The formalism is exemplified in two simple physical scenarios and we outline differences of the ab initio results to standard model assumptions, including frequency-dependent couplings and cross-mode decay terms, which may lead to qualitatively new effects in certain regimes.