  Equilibrium Bose-Einstein condensation of exciton-polaritons, demonstrated
with a long-lifetime microcavity [Phys. Rev. Lett. 118, 016602 (2017)], has
proven that driven-dissipative systems can undergo thermodynamic phase
transitions in the limit where the quasiparticle lifetime exceeds the
thermalization time. Here, we identify the role of dimensionality and polariton
interactions in determining the degree of thermalization in optically generated
traps. To distinguish the effect of trapping from interactions and lifetimes,
we measured the polariton distribution under four nonresonant Gaussian pumps in
a square geometry and compared it with polariton distributions measured with
each pump individually. We found that significant redistribution of polaritons
arises by trapping and modification of the density of states. Surprisingly
efficient polariton-polariton scattering below the condensation threshold is
evidenced by the depletion of the inflection-point polaritons. Our work
provides a deeper understanding of polariton distributions and their
interactions under various geometries of optically generated potentials.
