Intersubband polaritons in the electrical dipole gauge

We provide a theoretical description of the coupling between the electromagnetic field and the intersubband excitations of a bidimensional electron gas. Our theory, based on the electrical dipole gauge, applies generally to an arbitrary quantum heterostructure embedded in a multilayer waveguide or in a microcavity. We show that the dipole gauge Hamiltonian takes into account the Coulomb interactions in the system, without the need of adding extra terms to the Hamilitonian. Furthermore, the bright excitations of the system appear as many-body collective plasmon modes, interacting between each other and with the light field through dipole coupling. The electrical dipole gauge therefore provides a suitable framework for the study of solid-state quantum electrodynamics phenomena that occur at very high electronic densities, such as the ultrastrong light-matter interaction.