Eur. Phys. J. B (2018) 91: 180
https://doi.org/10.1140/epjb/e2018-90177-6

Regular Article

Light-matter interactions via the exact factorization approach^★

¹ Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
² Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York 10065, USA
³ The Physics Program and the Chemistry Program of the Graduate Center of the City University of New York, New York 10065, USA
⁴ Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

^a e-mail: Norah-Magdalena.Hoffmann@mpsd.mpg.de
^b e-mail: heiko.appel@mpsd.mpg.de
^c e-mail: angel.rubio@mpsd.mpg.de
^d e-mail: nmaitra@hunter.cuny.ed

Received: 16 March 2018
Received in final form: 1 June 2018
Published online: 6 August 2018

Abstract

The exact factorization approach, originally developed for electron-nuclear dynamics, is extended to light-matter interactions within the dipole approximation. This allows for a Schrödinger equation for the photonic wavefunction, in which the potential contains exactly the effects on the photon field of its coupling to matter. We illustrate the formalism and potential for a two-level system representing the matter, coupled to an infinite number of photon modes in the Wigner-Weisskopf approximation, as well as to a single mode with various coupling strengths. Significant differences are found with the potential used in conventional approaches, especially for strong couplings. We discuss how our exact factorization approach for light-matter interactions can be used as a guideline to develop semiclassical trajectory methods for efficient simulations of light-matter dynamics.