  Bosonic condensates of exciton polaritons (light-matter quasiparticles in a
semiconductor) provide a solid-state platform for studies of non-equilibrium
quantum systems with a spontaneous macroscopic coherence. These driven,
dissipative condensates typically coexist and interact with an incoherent
reservoir, which undermines measurements of key parameters of the condensate.
Here, we overcome this limitation by creating a high-density exciton-polariton
condensate in an optically-induced "box" trap. In this so-called Thomas-Fermi
regime, the condensate is fully separated from the reservoir and its behaviour
is dominated by interparticle interactions. We use this regime to directly
measure the polariton-polariton interaction strength, and reduce the existing
uncertainty in its value from four orders of magnitude to within three times
the theoretical prediction. The Thomas-Fermi regime has previously been
demonstrated only in ultracold atomic gases in thermal equilibrium. In a
non-equilibrium exciton-polariton system, this regime offers a novel
opportunity to study interaction-driven effects unmasked by an incoherent
reservoir.
