Coherence measurements of exciton-polaritons in thermal equilibrium reveal a new power law for two-dimensional condensates*

We report recent progress on the measurement of the coherent fraction of a two-dimensional Bose gas in thermal equilibrium. We have created a homogeneous exciton-polariton gas in equilibrium, realizing the textbook paradigm of a uniform Bose Gas in two-dimensions. Under these conditions, we have measured coherent fraction of this Bose gas from very low density up to density well above the condensation threshold. These measurements reveal a consistent power law for the coherent fraction over nearly three orders of magnitude of density variation. The same power law is seen in numerical simulations solving the two-dimensional Gross-Pitaevskii equation for the equilibrium coherence. This power law has not been predicted by prior analytical theories.