title: Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space.
abstract: The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.
authors.affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin-Dahlem, Germany;
authors.forename: Johannes
authors.initials: J
authors.lastname: Flick
authors.affiliation: Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria; Center for Free-Electron Laser Science & Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany;
authors.forename: Michael
authors.initials: M
authors.lastname: Ruggenthaler
authors.affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin-Dahlem, Germany; Center for Free-Electron Laser Science & Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany;
authors.forename: Heiko
authors.initials: H
authors.lastname: Appel
authors.affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin-Dahlem, Germany; Center for Free-Electron Laser Science & Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany; Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales, Universidad del País Vasco, 20018 San Sebastián, Spain angel.rubio@mpsd.mpg.de.
authors.forename: Angel
authors.initials: A
authors.lastname: Rubio
keywords: photon matter correlations; quantum electrodynamical density functional theory; quantum electrodynamics; strong light matter interaction; time-dependent density functional theory