Abstract
We present a theoretical description of the coupling between longitudinal optical phonons and collective excitations of a two-dimensional electron gas. By diagonalizing the Hamiltonian of the system, including Coulomb electron-electron and Fr\"ohlich interactions, we observe the formation of multisubband polarons, mixed states partially phonon and partially multisubband plasmon, characterized by a coupling energy which is a significant fraction, up to ~40%, of the phonon energy. We demonstrate that multisubband plasmons and longitudinal optical phonons are in the ultra-strong coupling regime in several III-V and II-VI material systems.