Nonadiabatic effects appear due to avoided crossings or conical intersections (CIs) 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 fieldmatter states called polaritons. In the present theoretical study we go further and create CIs in diatomics by means of a radiation field in the framework of cavity quantum electrodynamics. 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 CIs. First, the pronounced difference between the the quantum light-induced avoided crossing and the CI 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.The dynamics initiated in a molecule by absorbing a photon is often described in the Born-Oppenheimer (BO) or adiabatic approximation [1], where the electronic and nuclear degrees of freedom are treated separately. However, in some nuclear configurations called conical intersections (CIs) the mixing between the electronic and nuclear motions are very significant [2][3][4][5][6]. Owing to the strong nonadiabatic couplings (NACs) in the close vicinity of these CIs the BO approximation breaks down. It is well-known that these CIs have a significant impact on several important photo-dynamical processes, such as vision, photosynthesis, molecular electronics, and the photochemistry of DNA [7][8][9][10][11]. During the dynamics the CIs can serve as efficient decay channels for the ultrafast transfer of the populations. In the following we call these CIs, which originate from the field free electronic structure, natural CIs.Nonadiabatic effects can also appear when molecules are exposed to resonant laser light. The electric field can couple to two or more electronic states of the molecule via the non-vanishing transition dipole moment(s) [12][13][14][15]. This results either in a light-induced avoided crossing (LIAC) or a light-induced conical intersection (LICI) depending on how many nuclear degrees of freedom are involved in the field induced process [16]. In case of poly atomic molecules a sufficient number of vibrational degrees of freedom are always present to span a twodimensional branching space (BS), which is indispensable to the formation of LICI. In the case of diatomics one always has to find a proper second degree of freedom (DOF) which can act as a dynamical variable to form a BS. As the molecule rotates [17][18][19], the rotational angle between the molecular axis and the light polarization axis can serve as the missing DOF for establishing the BS [20].Nonadiabatic effects can arise in an optical or mi...