  Nonadiabatic effects appear due to avoided crossings or conical intersections
that are either intrinsic properties in field-free space or induced by a
classical laser field in a molecule. It was demonstrated that avoided crossings
in diatomics can also be created in an optical cavity. Here, the quantized
radiation field mixes the nuclear and electronic degrees of freedom creating
hybrid field-matter states called polaritons. In the present theoretical study
we go further and create conical intersections in diatomics by means of a
radiation field in the framework of cavity quantum electrodynamics (QED). By
treating all degrees of freedom, that is the rotational, vibrational,
electronic and photonic degrees of freedom on an equal footing we can control
the nonadiabatic quantum light-induced dynamics by means of conical
intersections. First, the pronounced difference between the the quantum
light-induced avoided crossing and the conical intersection with respect to the
nonadiabatic dynamics of the molecule is demonstrated. Second, we discuss the
similarities and differences between the classical and the quantum field
description of the light for the studied scenario.
