  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.
