Electrically tuneable exciton-polaritons through free electron doping in monolayer WS$_2$ microcavities

We demonstrate control over light-matter coupling at room temperature combining a field effect transistor (FET) with a tuneable optical microcavity. Our microcavity FET comprises a monolayer tungsten disulfide WS$_2$ semiconductor which was transferred onto a hexagonal boron nitride flake that acts as a dielectric spacer in the microcavity, and as an electric insulator in the FET. In our tuneable system, strong coupling between excitons in the monolayer WS$_2$ and cavity photons can be tuned by controlling the cavity length, which we achieved with excellent stability, allowing us to choose from the second to the fifth order of the cavity modes. Once we achieve the strong coupling regime, we then modify the oscillator strength of excitons in the semiconductor material by modifying the free electron carrier density in the conduction band of the WS$_2$. This enables strong Coulomb repulsion between free electrons, which reduces the oscillator strength of excitons until the Rabi splitting completely disappears. We controlled the charge carrier density from 0 up to 3.2 $\times$ 10$^{12}$ cm$^{-2}$, and over this range the Rabi splitting varies from a maximum value that depends on the cavity mode chosen, down to zero, so the system spans the strong to weak coupling regimes.