  The elementary optical excitations of a two-dimensional electron or hole
system have been identified as exciton-Fermi-polarons. Nevertheless, the
connection between the bound state of an exciton and an electron, termed trion,
and exciton-polarons is subject of ongoing debate. Here, we use an analogy to
the Tavis-Cummings model of quantum optics to show that an exciton-polaron can
be understood as a hybrid quasiparticle -- a coherent superposition of a bare
exciton in an unperturbed Fermi sea and a bright collective excitation of many
trions. The analogy is valid to the extent that the Chevy Ansatz provides a
good description of dynamical screening of excitons and provided the Fermi
energy is much smaller than the trion binding energy. We anticipate our results
to bring new insight that could help to explain the striking differences
between absorption and emission spectra of two-dimensional semiconductors.
