Microscopic Theory of Polaron-Polariton Dispersion and Propagation

We develop an analytical, microscopic theory to describe polaron-polariton dispersion, formed by hybridizing excitons, photons, and phonons, as well as their coherent dynamics inside optical cavities. Starting from a microscopic light-matter Hamiltonian, we derive a simple analytical model by employing a nonperturbative treatment of the phonon and photon couplings to excitons. Within our theoretical framework, phonons are treated as classical fields, which are then quantized via the Floquet formalism. We show that, to a good approximation, the entire polaron-polariton system can be described with a band picture despite the phonons breaking translational symmetry. Our theory also sheds light on the long-lived coherent ballistic motion of exciton-polaritons with high excitonic character that propagate with group velocities lower than expected from pure exciton-polariton bands, offering a microscopic explanation for these puzzling experimental observations.