  Bose Einstein condensation of exciton-polaritons has recently been reported
in homogeneous structures only affected by random in-plane fluctuations. We
have taken advantage of the ubiquitous defects in semiconductor microcavities
to reveal the spontaneous dynamical condensation of polaritons in the quantised
levels of a trap. We observe condensation in several quantized states, taking
their snapshots in real and reciprocal space. We show also the effect of
particle interactions for high occupations numbers, revealed by a change in the
confined wave function toward the Thomas Fermi profile.
