  The elementary optical excitations of a two-dimensional electron system
strongly coupled to a microcavity are trion-polaritons. Using a variational
approach, we demonstrate that the competition between Coulomb interaction and
light-matter coupling plays a crucial role in determining the lowest-energy
orbital and spin properties of trion-polaritons. When the light-matter
interaction exceeds the bare trion binding, singlet and triplet trion states
are mixed due to a cavity-mediated spin-orbit effect, which in turn results in
a strong increase of the outer electron Bohr radius. In this strong cavity
coupling regime, the trion-polariton consists of an exciton-polariton
surrounded by a weakly bound electron and is reminiscent of a coherent Rydberg
excitation.
