  We have performed real and momentum space spin-dependent spectroscopy of
spontaneously formed exciton polariton condensates for a non-resonant pumping
scheme. Under linearly polarized pump, our results can be understood in terms
of spin-dependent Boltzmann equations in a two-state model. This suggests that
relaxation into the ground state occurs after multiple phonon scattering events
and only one polariton-polariton scattering. For the circular pumping case, in
which only excitons of one spin are injected, a bottleneck effect is observed,
implying inefficient relaxation.
