Abstract
We present a many-body theory for the interactions of two-dimensional exciton-polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the exciton-exciton scattering is strongly renormalized by the light-matter coupling and acquires an inverse logarithmic dependence on the lower polariton energy. As a result, the polariton interaction strength may be enhanced at red photon-exciton detuning when the exciton-exciton scattering length is large. We also derive the exact Tan relations for exciton-polaritons, calculate Tan's contact coefficient and find an even more significant enhancement. Our predictions may provide a qualitatively correct guide for studies of exciton and polariton nonlinearities and suggest a route to achieving strongly nonlinear polariton gases.
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