  In transition metal dichalcogenides layers of atomic scale thickness, the
electron-hole Coulomb interaction potential is strongly influenced by the sharp
discontinuity of the dielectric function across the layer plane. This feature
results in peculiar non-hydrogenic excitonic states, in which exciton-mediated
optical nonlinearities are predicted to be enhanced as compared to their
hydrogenic counterpart. To demonstrate this enhancement, we performed optical
transmission spectroscopy of a MoSe$_2$ monolayer placed in the strong coupling
regime with the mode of an optical microcavity, and analyzed the results
quantitatively with a nonlinear input-output theory. We find an enhancement of
both the exciton-exciton interaction and of the excitonic fermionic saturation
with respect to realistic values expected in the hydrogenic picture. Such
results demonstrate that unconventional excitons in MoSe$_2$ are highly
favourable for the implementation of large exciton-mediated optical
nonlinearities, potentially working up to room temperature.
