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We provide a theoretical description for the coupling between theintersubband excitations of a bi-dimensional electron gas with theelectromagnetic field. This description, based on the electrical dipole gauge,applies to an arbitrary quantum heterostructure embedded in a generalmultilayered waveguide or a microcavity. We show that the dipole gaugeHamiltonian automatically takes into account the Coulomb interactions in thissystem. Furthermore, it can be conveniently expressed in terms of the many-bodycollective plasmon modes, which interact both with each other and with thelight field. The dipole gauge therefore provides a suitable framework for thestudy of solid state Quantum Electrodynamics (QED) phenomena, such as theultra-strong light-matter interaction regime, occurring at very high electronicdensities.

Intersubband Polaritons in the Electrical Dipole Gauge