  The optical Stark effect is a tell-tale signature of coherent light-matter
interaction in excitonic systems, wherein an irradiating light beam tunes
exciton transition frequencies. Here we show that, when excitons are placed in
a nanophotonic cavity, the excitonic Stark effect can become highly nonlinear,
exhibiting multi-valued and hysteretic Stark shifts that depend on the history
of the irradiating light. This multistable Stark effect (MSE) arises from
feedback between the cavity mode occupation and excitonic population, mediated
by the Stark-induced mutual tuning of the cavity and excitonic resonances.
Strikingly, the MSE manifests even for very dilute exciton concentrations and
can yield discontinuous Stark shift jumps of order meV. We expect that the MSE
can be realized in readily available transition metal dichalcogenide excitonic
systems placed in planar photonic cavities, at modest pump intensities. This
phenomenon can provide new means to engineer coupled states of light and matter
that can persist even in the single exciton limit.
