  The nature of trions and their interaction with light has remained a puzzle.
The composition and dispersion of polaritons involving trions provide insights
into this puzzle. Trions and excitons in doped two-dimensional (2D) materials
are not independent excitations but are strongly coupled as a result of Coulomb
interactions. When excitons in doped 2D materials are also strongly coupled
with light inside an optical waveguide, the resulting polariton states are
coherent superpositions of exciton, trion, and photon states. We realize these
exciton-trion-polaritons by coupling an electron-doped monolayer of
two-dimensional material MoSe2 to the optical mode in a photonic crystal
waveguide. Our theoretical model, based on a many-body description of these
polaritons, reproduces the measured polariton energy band dispersion and Rabi
splittings with excellent accuracy. Our work sheds light on the structure of
trion states in 2D matrials and also on the indirect mechanism by which they
interact with light.
