Tunable optical nonlinearity for transition metal dichalcogenide polaritons dressed by a Fermi sea

We study the system of a transition metal dichalcogenide (TMD) monolayer placed in an optical resonator, where the strong light-matter coupling between excitons and photons is achieved. We present a quantitative theory of the nonlinear optical response for exciton-polaritons for the case of a 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.