  We consider the problem of a coherently driven polariton box cavity in the
low driving regime, accounting for the polarization degree of freedom. The
different interaction strengths between co- and cross-circularly polarized
polaritons and a realistic linear-polarization splitting allows one to model
the system as two coupled nonlinear resonators with both self- and
cross-Kerr-like nonlinearities, thus making our results potentially relevant
for other experimental platforms. Within an effective wave-function approach,
we obtain analytical expressions for the steady-state polarization-resolved
polariton populations and second-order correlation functions, which agree very
well with our numerical results obtained from a Lindblad master equation.
Notably, we highlight that depending on the excitation polarization (circular
or linear), both the unconventional (interference-mediated) and conventional
(mediated by nonlinearities) antibunchings can be investigated in a single
cavity. Moreover, using our results, we argue that recent experiments on
confined fiber-cavity polaritons are likely to have probed a regime where the
dominant interaction is between cross-polarized polaritons, which is
characteristic of the polariton Feshbach resonance. We furthermore investigate
the regime close to resonance using a two-channel model, and we show that
systems with large biexciton binding energies, such as atomically thin
semiconductors, are promising platforms for realizing strong polariton
antibunching.
