FEW-PHOTON TRANSPORT IN STRONGLY INTERACTING LIGHT-MATTER SYSTEMS: A SCATTERING APPROACH

Abstract

Engineering strong photon-photon interactions at the quantum level have been crucial in various areas of research, notably in quantum information processing and quantum simulation. It is often done by coupling matter strongly to light. A promising way to achieve this is via waveguide quantum electrodynamics (QED). Motivated by these advancements, we study few-photon transport in waveguide QED setups. First, we present a diagrammatic technique to systematically study multiphoton scattering based on the scattering formalism and Green's function approach. We demonstrate our proposal through physically relevant examples involving scattering of few-photon states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators described by the Bose-Hubbard model. In the second part, we apply the diagrammatic technique that was developed to perform a comprehensive study on a Bose-Hubbard lattice with quasiperiodic potential. This model exhibits many-body localisation. We compute the two-photon transmission probability and show that it carries signatures of the underlying localisation transition with a close agreement to the participation ratio of the eigenstates. The systematic scattering approach provided in this thesis provides a foundation for future works at the interface between quantum optics and condensed matter.