  We consider a zigzag chain of coupled micropillar cavities, taking into
account the polarization of polariton states. We show that the TE-TM splitting
of photonic cavity modes yields topologically protected polariton edge states.
During the strongly non-adiabatic process of polariton condensation, the
Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to
dimerization of polymer chains. We show that dark-bright solitons appear as
domain walls between polarization domains, analogous to the
Su-Schrieffer-Heeger solitons in polymers. The soliton density scales as a
power law with respect to the quenching parameter.
