Mean-field mixed quantum-classical approach for many-body quantum dynamics of exciton polaritons

Coupling material excitations to photons inside optical cavities has been experimentally shown to give rise to a wide range of exotic quantum phenomena, and such light--matter hybrid systems have been proposed as versatile platforms for developing quantum devices. However, the theoretical understanding of the interplay between phonon-induced disorder and nonlinear many-body interactions, central to the dynamics of these systems, remains unclear, as incorporating these contributions into direct quantum dynamical simulations is highly challenging. To address this, the authors develop here a mean-field many-body mixed quantum--classical approach, in which the nuclei are propagated quasiclassically while the electronic and photonic degrees of freedom evolve under a nonlinear Schr\"odinger equation that incorporates many-body effects at the mean-field level. Using this framework, the authors demonstrate that nonlinear interactions and the total number of excitations can be tuned to enhance quantum coherence in light--matter systems and enable enhanced exciton transport in materials placed inside optical cavities.