Microscopic calculation of polariton scattering in semiconductor microcavities

Recent experiments in exciton-polariton systems have provided high-precision measurements of the value of the polariton-polariton interaction constant, which is a key parameter that governs the nonlinear dynamics of polariton condensates and potentially enables quantum correlated polaritons. Yet, until now, this parameter has only been addressed theoretically using perturbative treatments or approximations that do not include the composite nature of the excitons. Here, we use a recently developed microscopic description of polaritons involving electrons, holes, and photons, where the interactions between charged particles are assumed to be highly screened. Within this model, we perform an exact four-body calculation of the spin-polarized polariton-polariton and polariton-exciton interaction constants. In the limit of weak light-matter coupling relevant to an atomically thin semiconductor in a microcavity, we obtain excellent agreement with a recently proposed universal form of low-energy polariton-polariton scattering [O. Bleu et al., Phys. Rev. Res. 2, 043185 (2020)]. At stronger light-matter coupling, of relevance to multilayer microcavities, we observe that the interaction constant increases towards that predicted by the Born approximation. We show that in all regimes of interest the interaction constant can be accurately obtained from the exciton-exciton scattering phase shift at negative collision energy, and we argue that this has important implications for interactions in other systems featuring strong light-matter coupling.