  We present a microscopic theory describing the stimulated scattering of
intersubband polariton excitations in a microcavity-embedded two-dimensional
electron gas. In particular, we consider the polariton scattering induced by
the spontaneous emission of optical phonons. Our theory demonstrates the
possibility of final-state stimulation for the scattering of such composite
excitations, accounting for the deviations from perfect bosonicity occurring at
high excitation densities. By using realistic parameters for a GaAs
semiconductor system, we predict how to achieve a quantum degenerate regime,
leading to ultralow threshold lasing without population inversion.
