  We investigate the optical orientation, polarization pinning, and
depolarization of optically confined semiconductor exciton-polariton
condensates. We perform a complete mapping of the condensate polarization as a
function of incident nonresonant excitation polarization and power. We utilize
a ring-shaped excitation pattern to generate an exciton-induced potential that
spatially confines polariton condensates into a single mode. We observe that
formation of circular polarization in the condensate persists even for a weakly
cocircularly polarized pump. By varying the excitation ring diameter we realize
a transition from the condensate polarization being pinned along the
coordinate-dependent cavity-strain axes, to a regime of zero degree of
condensate polarization. Analysis through the driven-dissipative stochastic
Gross-Pitaevskii equation reveals that this depolarization stems from a
competition between sample induced in-plane polarization splitting and the
condensate-reservoir overlap. An increase in the role of the latter results in
weakening of the condensate fixed-point phase space attractors, and enhanced
random phase space walk and appearance of limit cycle trajectories, reducing
the degree of time-integrated polarization.
