  The generation of squeezed light in semiconductor materials opens
opportunities for building on-chip devices that are operated at the quantum
level. Here we study theoretically a squeezed light source of polariton dark
solitons confined in a geometric potential well of semiconductor microcavities
in the strong coupling regime. We show that polariton dark solitons of odd and
even parities can be created by tuning the potential depth. When driving the
potential depth linearly, a bistability of solitons with the two different
parities can be induced. Strong intensity squeezing is obtained near the
turning point of the bistability due to the large nonlinear interaction, which
can be controlled by Feshbach resonance. The phase diagram of the bistability
and squeezing of the dark solitons is obtained through large scale numerical
calculations. Our study contributes to the current efforts in realizing
topological excitations and squeezed light sources with solid-state devices.
