  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.
