  We investigate theoretically the polariton coupling between the light
confined in a planar cavity and the intersubband transitions of a
two-dimensional electron gas confined in semiconductor quantum wells in the
presence of a vertical magnetic field. We show that in heterostructures made of
non-parabolic semiconductors, the polaritons do not fit a two-level problem,
since the cavity photons couple to a non-degenerate ensemble of intersubband
transitions. As a consequence, the stationary polariton eigenstates become very
sensitive to the vertical magnetic field, which thus plays the role of an
external parameter that controls the regime of light-matter interactions. At
intermediate field strength we predict that the magneto-polaritons have energy
dispersions ideally suited to parametric amplification.
