  We demonstrate that a ionising transition can be strongly coupled to a
photonic resonance. The strong coupling manifests itself with the appearance of
a narrow optically active resonance below the ionisation threshold. Such a
resonance is due to electrons transitioning into a novel bound state created by
the collective coupling of the electron gas with the vacuum field of the
photonic resonator. Applying our theory to the case of bound-to-continuum
transitions in microcavity-embedded doped quantum wells, we show how those
strong-coupling features can be exploited as a novel knob to tune both optical
and electronic properties of semiconductor heterostructures.
