Microscopic Theory of Polariton Group Velocity Renormalization

Cavity exciton-polaritons exhibit ballistic transport and can achieve a distance of 100 $\mu $m in one picosecond. This ballistic transport significantly enhances mobility compared to that of bare excitons, which often move diffusively and become the bottleneck for energy conversion and transfer devices. Despite being robustly reproduced in experiments and simulations, there is no comprehensive microscopic theory addressing the group velocity of polariton transport, and its renormalization due to phonon scattering while still preserving this ballistic behavior. In this work, we develop a microscopic theory to describe the group velocity renormalization using a finite-temperature Green's function approach. Utilizing the generalized Holstein-Tavis-Cummings Hamiltonian, we analytically derive an expression for the group velocity renormalization and find that it is caused by phonon-mediated transitions from the lower polariton (LP) states to the dark states, then scattering from dark states back to LP. The dark states do not have to be populated in this process, serving as the virtual state for super-exchange (especially true for a large light-matter detuning). The theory predicts that the magnitude of group velocity renormalization scales linearly with the phonon bath reorganization energy under weak coupling conditions (perturbative regime for exciton-phonon coupling) and also linearly depends on the temperature in the high-temperature regime. These predictions are numerically verified using quantum dynamics simulations, demonstrating quantitative agreement. Our findings provide theoretical insights and a predictive analytical framework that advance the understanding and design of cavity-modified semiconductors and molecular ensembles, opening new avenues for engineered polaritonic devices.