Many-body effects of a two-dimensional electron gas on trion-polaritons

We theoretically investigate the trion-polariton and the effects of a two-dimensional electron gas on its single-particle properties. Focusing on the trion and exciton transitions, we set up an effective model and calculate the optical absorption of the quantum well containing the two-dimensional electron gas (2DEG). Including the light-matter coupling, we compute the Rabi splitting and polariton line shapes as a function of 2DEG density. The role of finite temperature is investigated. The spatial extent of the trion-polariton is also calculated. We find a substantial charge buildup at short distances as long as the Rabi frequency does not exceed the trion binding energy. All our calculations take into account the Fermi edge singularity and the Anderson orthogonality catastrophe.