  We study a system of a transition metal dichalcogenide (TMD) monolayer placed
in an optical resonator, where strong light-matter coupling between excitons
and photons is achieved. We present quantitative theory of the nonlinear
optical response for exciton-polaritons for the case of doped TMD monolayer,
and analyze in detail two sources of nonlinearity. The first nonlinear response
contribution stems from the Coulomb exchange interaction between excitons. The
second contribution comes from the reduction of Rabi splitting that originates
from phase space filling at increased exciton concentration and the composite
nature of excitons. We demonstrate that both nonlinear contributions are
enhanced in the presence of free electrons. As free electron concentration can
be routinely controlled by an externally applied gate voltage, this opens a way
of electrical tuning of the nonlinear optical response.
