  Integration of 2D semiconductors with photonic crystal slabs provides an
attractive approach to achieve strong light--matter coupling and
exciton-polariton formation in a planar chip-compatible geometry. However, for
the development of practical devices, it is crucial that the polariton
excitations in the structure are easily tunable and exhibit strong nonlinear
response. Here we study neutral and charged exciton-polaritons in an
electrostatically gated planar photonic crystal slab with an embedded monolayer
semiconductor MoSe$_2$ and experimentally demonstrate strong polariton
nonlinearity, which can be tuned via gate voltage. We find that modulation of
dielectric environment within the photonic crystal results in the formation of
two distinct resonances with significantly different nonlinear response, which
enables optical switching with ultrashort laser pulses. Our results open new
avenues towards development of active polaritonic devices in a compact
chip-compatible implementation.
