  The exact factorization approach, originally developed for electron-nuclear
dynamics, is extended to light-matter interactions within the dipole
approximation. This allows for a Schrodinger 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 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.
