  We present a theoretical study of the optical response of a nonlinear
oscillator formed by coupling a metal nanoparticle local surface plasmon
resonance to excitonic degrees of freedom in a monolayer transition-metal
dichalcogenide. We show that the combined system should exhibit strong
anharmonicity in its low-lying states, predicting for example a seven
order-of-magnitude increase in nonlinearity relative to a silicon photonic
crystal cavity. Then, we demonstrate that such system exhibits strong quantum
features such as antibunching and non-Gaussianity. Arrays of such nanoscale
nonlinear oscillators could be used to realize novel optical metamaterials;
alternatively, an individual nanoparticle-monolayer construct could be coupled
to an optical resonator to mediate efficient input-output coupling to
propagating fields.
