  Due to the hybridization of charged excitons with cavity photons,
trion-polaritons (TP) in microcavity semiconductors are a promising avenue for
realizing strong polariton interactions and many-body polariton phases. We
develop a quantum field theoretical formalism to study the formation of
trion-polaritons in a microcavity semiconductor doped with itinerant electrons
within the ultra-strong light-matter coupling regime. We predict a new class of
many-body states resulting from the intriguing interplay of polarons and
virtual photons in an uncharted territory of light-matter interactions and
Feshbach physics.
