AbstractThe problem of parametric excitation of electromagnetic vibrations of a quantum electron‐phonon system is studied using a formalism based on the equation of motion for the quantum distribution function of an electron gas interacting with phonons in the presence of high‐intensity radiation field and the complete system of Maxwell equations. Calculations of the growth rates and the threshold values of the external electric field E0 are presented for both, uncoupled electron and electron‐phonon systems in different regions of wave number κ for κ ‖ E0 as well as for κ ⊥ E/0.