  Nonlinear optical effects such as four-wave mixing and generation of squeezed
light are ubiquitous in optical devices and light sources. For new devices
operating at low optical power, the resonant nonlinearity arising from the
two-photon sensitive bound biexciton in a semiconductor microcavity is an
interesting prospective platform. Due to the particularly strong Coulomb
interaction in atomically thin semiconductors, these materials have strongly
bound biexcitons and operate in the visible frequency range of the
electromagnetic spectrum. To remove the strong pump laser from the generated
light in optical devices or to simultaneously excite non-degenerate polaritons,
a bichromatic-pump configuration with two spectrally separated pump lasers is
desirable. In this paper, we theoretically investigate spontanous four-wave
mixing and quadrature-squeezing in a bichromatically pumped atomically thin
semiconductor microcavity. We explore two different configurations that support
degenerate and non-degenerate scattering from polaritons into bound biexcitons,
respectively. We find that these configurations lead to the generation strongly
single- and two-mode quadrature-squeezed light.
